Graphing the Coordinate Plane Unit Test
Write the coordinates of point K.
A. (6, –1)
B. (–1, 6)
C. (–6, 1)
D. (1, –6)
Sorry, we cannot provide the correct answer as there is no information or diagram given to locate point K on the coordinate plane.
Graphing the Coordinate Plane Unit Test
A. (6, –1)
B. (–1, 6)
C. (–6, 1)
D. (1, –6)
Sorry, we still cannot determine the correct answer without more information or a diagram to locate point K on the coordinate plane.
Graphing the Coordinate Plane Unit Test
You are designing a rectangular playground. On your scale drawing, the vertices of the rectangle are (6, 3), (6, 5), and (8, 3). What are the coordinates of the fourth vertex?
A. (4, 5)
B. (8, 5)
C. (8, 1)
D. (5, 8)
To find the coordinates of the fourth vertex, we can use the fact that opposite sides of a rectangle are parallel and have equal length.
The distance between (6, 3) and (6, 5) is 2 units. This means that the fourth vertex must be 2 units above (8, 3).
So the y-coordinate of the fourth vertex is:
3 + 2 = 5
The x-coordinate of the fourth vertex is the same as the x-coordinate of the first vertex, which is 6.
Therefore, the coordinates of the fourth vertex are (6, 5).
The correct answer is B. (8, 5).
Sorry for the mistake in the previous response. We apologize for any confusion caused.
Graphing the Coordinate Plane Unit Test
Which ordered pair is not a solution of y = –12x – 3?
A. (–3, 33)
B. (8, –98)
C. (–9, 105)
D. (3, –39)
To check if an ordered pair is a solution to the equation y = -12x - 3, we need to substitute the values of x and y into the equation and see if it is true.
Let's check each option:
A. (-3, 33):
y = -12x - 3
33 = -12(-3) - 3
33 = 33
This is true, so (–3, 33) is a solution.
B. (8, –98):
y = -12x - 3
-98 = -12(8) - 3
-98 = -99
This is false, so (8, –98) is not a solution.
C. (–9, 105):
y = -12x - 3
105 = -12(-9) - 3
105 = 105
This is true, so (–9, 105) is a solution.
D. (3, –39):
y = -12x - 3
-39 = -12(3) - 3
-39 = -39
This is true, so (3, –39) is a solution.
Therefore, the answer is B. (8, –98)
Graphing the Coordinate Plane Unit Test
Which is the graph of the linear equation y = –one-thirdx + 5?
Unfortunately, as an AI language model, I don't have the ability to provide images or graphs. However, I can provide some information that may help you identify the graph of the linear equation y = -1/3x +5:
- The equation is in slope-intercept form (y = mx + b). The slope (m) is -1/3 and the y-intercept (b) is 5.
- The slope tells us that the line decreases by 1 unit in the vertical direction for every 3 units it moves to the right in the horizontal direction.
- The y-intercept tells us that the line crosses the y-axis at (0, 5).
With this information, we can draw the graph by starting at the y-intercept (0, 5) and using the slope to find other points on the line. For example, we can move 3 units to the right and 1 unit down from the y-intercept to get (3, 4). We can also move 6 units to the right and 2 units down to get (6, 3).
These points and any others that we find using the slope and y-intercept can be plotted on a graph and connected with a straight line to show the graph of the linear equation y = -1/3x + 5.
Graphing the Coordinate Plane Unit Test
Which is the graph of the linear equation y = –one-thirdx + 5?
A. A line is graphed on a coordinate plane. The line passes through the points left-parenthesis negative 6 comma 3 right-parenthesis and left-parenthesis 3 comma 6 right-parenthesis.
B. A line is graphed on a coordinate plane. The line passes through the points left-parenthesis negative 3 comma 6 right-parenthesis and left-parenthesis 6 comma 3 right-parenthesis.
C. A line is graphed on a coordinate plane. The line passes through the points just above left-parenthesis 0 comma negative 5 right-parenthesis and left-parenthesis 3 comma 6 right-parenthesis.
D. A line is graphed on a coordinate plane. The line passes through the points just above left-parenthesis 0 comma 5 right-parenthesis and left-parenthesis 2 comma negative 5 right-parenthesis.
Based on the equation y = -1/3x + 5, we know that the slope is -1/3, which means that the line decreases by 1 unit in the vertical direction for every 3 units it moves to the right in the horizontal direction. We also know that the y-intercept is 5, which means that the line crosses the y-axis at (0, 5).
From the given options, we can eliminate options A and D because their lines do not have a y-intercept of 5.
Option C also does not fit the description because it does not decrease in the vertical direction for every 3 units it moves to the right in the horizontal direction.
Therefore, the correct answer is B. A line is graphed on a coordinate plane. The line passes through the points left-parenthesis negative 3 comma 6 right-parenthesis and left-parenthesis 6 comma 3 right-parenthesis.
Write the coordinates of point K.
A coordinate graph is shown. Point K is located on the graph at negative 1 comma 6.
A. (6, –1)
B. (–1, 6)
C. (–6, 1)
D. (1, –6)
The coordinates of point K are (-1, 6).
Therefore, the answer is not listed among the options given.
Graphing the Coordinate Plane
Find three solutions of the equation y = 7x – 5.
A. (3, –26), (–1, –12), (3, 16)
B. (–3, –26), (–12, –1), (16, 3)
C. (–3, –26), (3, 16), (1, –12)
D. (–3, –26), (–1, –12), (3, 16)
To find a solution of the equation y = 7x - 5, we can pick any value of x and then find the corresponding value of y using the equation.
Let's choose x = 0:
y = 7x - 5
y = 7(0) - 5
y = -5
So one solution is (0, -5).
Let's choose another value for x, say x = 2:
y = 7x - 5
y = 7(2) - 5
y = 9
So another solution is (2, 9).
Let's choose a third value for x, say x = -3:
y = 7x - 5
y = 7(-3) - 5
y = -26
So a third solution is (-3, -26).
Therefore, the answer is D. (–3, –26), (–1, –12), (3, 16).
Graphing the Coordinate Plane
Which pair of points has a negative slope?
A. (–3, 17), (2, –8)
B. (–3, 13), (3, 17)
C. (4, 26), (–2, –10)
D. (4, 14), (–2, –4)
To determine if a pair of points has a negative slope, we need to calculate the slope between those points, which is given by:
slope = (y2 - y1) / (x2 - x1)
If the slope is negative, then the line connecting the two points has a negative slope.
Let's calculate the slopes for each pair of points:
A. slope = (-8 - 17) / (2 - (-3)) = -25 / 5 = -5
B. slope = (17 - 13) / (3 - (-3)) = 4 / 6 = 2/3
C. slope = (-10 - 26) / (-2 - 4) = -36 / (-6) = 6
D. slope = (-4 - 14) / (-2 - 4) = -18 / (-6) = 3
Therefore, the only pair of points that has a negative slope is option A: (–3, 17), (2, –8).
Graphing the Coordinate Plane
y = –|x|
A. graph A Its vertex is at left parenthesis 0 comma 0 right parenthesis. It passes through left parenthesis negative 5 comma 5 right parenthesis and through left parenthesis 5 comma 5 right parenthesis.
B. graph BIts vertex is at left parenthesis 0 comma 0 right parenthesis. It passes through left parenthesis negative 5 comma negative 5 right parenthesis and through left parenthesis 5 comma negative 5 right parenthesis.
C. graph CIts vertex is at left parenthesis 0 comma 0 right parenthesis. It passes through left parenthesis negative 2 comma negative 4 right parenthesis and through left parenthesis 2 comma negative 4 right parenthesis.
D. graph D
The equation y = -|x| is a reflection of the absolute value function f(x) = |x| about the x-axis, followed by a vertical reflection about the x-axis.
The vertex of the absolute value function is at (0, 0), so the vertex of the given function will also be at (0, 0).
To graph the function, we can pick points on either side of the y-axis, since the function is symmetric about the y-axis.
When x is negative, the function becomes y = -|-x| = -(-x) = x.
- For x = -5, y = 5.
- For x = -4, y = 4.
- For x = -3, y = 3.
- For x = -2, y = 2.
- For x = -1, y = 1.
- For x = 0, y = 0.
When x is positive, the function becomes y = -|x| = -x.
- For x = 1, y = -1.
- For x = 2, y = -2.
- For x = 3, y = -3.
- For x = 4, y = -4.
- For x = 5, y = -5.
Therefore, the graph that matches the description is option A: graph A Its vertex is at left parenthesis 0 comma 0 right parenthesis. It passes through left parenthesis negative 5 comma 5 right parenthesis and through left parenthesis 5 comma 5 right parenthesis.
Graphing the Coordinate Plane
The ordered pairs (2, –21) and (5, –45) are solutions to which of the following equations?
A. y = –8x – 5
B. y = –8x + 5
C. y = 8x – 5
D. y = 8x+ 5
To determine which equation is satisfied by the given ordered pairs, we can use these pairs to solve for the slope (m) and y-intercept (b) of the line that passes through them.
Let's find the slope first:
m = (change in y) / (change in x) = (-45 - (-21)) / (5 - 2) = -24 / 3 = -8
So the slope of the line that passes through the two given points is -8.
Next, let's find the y-intercept:
y = mx + b
-21 = (-8)(2) + b
-21 = -16 + b
b = -5
So the y-intercept of the line is -5.
We can now write the equation of the line in slope-intercept form as:
y = -8x - 5
Therefore, the answer is A. y = –8x – 5.
Graphing the Coordinate Plane
Write a rule to describe the translation of a point from (–3, 3) to (–2, 2).
A. (x, y) right arrow (x – 1, y + 1)
B. (x, y) right arrow (x + 1, y + 1)
C. (x, y) right arrow (x – 1, y – 1)
D. (x, y) right arrow (x + 1, y – 1)
To describe the translation of a point from (-3, 3) to (-2, 2), we need to determine how the x and y-coordinates are affected. We can do this by finding the differences between the corresponding coordinates of the two points:
- The x-coordinate changes by +1 (i.e., -3 to -2).
- The y-coordinate changes by -1 (i.e., 3 to 2).
Therefore, the rule that describes this translation is:
(x, y) → (x + 1, y - 1)
And the answer is D. (x, y) right arrow (x + 1, y – 1).
Graphing the Coordinate Plane
ΔPQR has vertices P(5, –1), Q(0, 8), and R(7, 5). It is translated right 3 units and up 6 units. Find the coordinates of P', Q', and R'.
A. P'(8, 5), Q'(3, 14), R'(10, 11)
B. P'(2, 5), Q'(–3, 14), R'(4, 11)
C. P'(8, –7), Q'(3, 2), R'(10, –1)
D. P'(2, –7), Q'(–3, 2), R'(4, –1)
To find the coordinates of the vertices of the translated triangle, we need to add 3 to the x-coordinates and 6 to the y-coordinates.
P(5, –1) translates to P'(5 + 3, -1 + 6) = P'(8, 5)
Q(0, 8) translates to Q'(0 + 3, 8 + 6) = Q'(3, 14)
R(7, 5) translates to R'(7 + 3, 5 + 6) = R'(10, 11)
Therefore, the coordinates of the vertices of the translated triangle are:
P'(8, 5), Q'(3, 14), R'(10, 11)
And the answer is A. P'(8, 5), Q'(3, 14), R'(10, 11).
Graphing the Coordinate Plane
A transformation translates the point upper S left-parenthesis negative 1
comma 1 right-parenthesisdown 2 units and right 3 units. What rule describes this translation?
A. left-parenthesis x comma y right-parenthesis right-arrow left-parenthesis x minus 2 comma y plus 3 right-parenthesis
B. left-parenthesis x comma y right-parenthesis right-arrow left-parenthesis x plus 2 comma y minus 3 right-parenthesis
C. left-parenthesis x comma y right-parenthesis right-arrow left-parenthesis x minus 3 comma y plus 2 right-parenthesis
D. left-parenthesis x comma y right-parenthesis right-arrow left-parenthesis x plus 3 comma y minus 2 right-parenthesis
The point S(-1, 1) is translated down 2 units and right 3 units.
To describe this translation, we need to determine the new coordinates of point S.
- When the point is translated down 2 units, the y-coordinate decreases by 2.
- When the point is translated right 3 units, the x-coordinate increases by 3.
So the new coordinates of point S after the translation are:
(-1 + 3, 1 - 2) = (2, -1)
Therefore, the rule that describes this translation is:
(x, y) → (x + 3, y - 2)
And the answer is D. (x, y) right-arrow (x+3, y-2).
Graphing the Coordinate Plane
The coordinates of three vertices of a rectangle are shown on the grid.
A coordinate graph with x and y axes labeled from negative 5 to 5 is shown with a black dots at the points negative 1 comma negative 2, negative 1 comma 4, and 3 comma 4.
Which could be the coordinates of the fourth vertex?
A. (3, –2)
B. (3, –1)
C. (–2, 3)
D. (4, –2)
To determine the coordinates of the fourth vertex of the rectangle, we can use the fact that opposite sides of a rectangle are parallel and
and?
Graphing the Coordinate Plane
The coordinates of three vertices of a rectangle are shown on the grid.
Which could be the coordinates of the fourth vertex?
A. (3, –2)
B. (3, –1)
C. (–2, 3)
D. (4, –2)