Use the graph to derive the equation of the line in slope-intercept form.
(1,3) and (0,-2)
First, let's calculate the slope of the line using the two given points (1,3) and (0,-2).
Slope (m) = (y2 - y1) / (x2 - x1)
= (-2 - 3) / (0 - 1)
= -5 / -1
= 5
Now, we can use the slope-intercept form of a line, y = mx + b, where m is the slope and b is the y-intercept.
We can choose one of the given points, say (1,3), to substitute into the equation.
3 = 5(1) + b
3 = 5 + b
b = 3 - 5
b = -2
Therefore, the equation of the line in slope-intercept form is y = 5x - 2.
Which linear equation represents this nonproportional linear relationship?
X= -5, 0, 2
Y= 0, 5, 7
A: y=-5x+5
B: y=-x+5
C: y=x+5
D: 1/5x+5
To determine which linear equation represents the nonproportional linear relationship between the given values of x and y, we first need to calculate the slope (m) using the two points provided: (x1, y1) = (-5, 0) and (x2, y2) = (0, 5).
Slope (m) = (y2 - y1) / (x2 - x1)
Slope (m) = (5 - 0) / (0 - (-5))
Slope (m) = 5 / 5
Slope (m) = 1
Since the slope is 1, we are looking for a linear equation in the form y = mx + b where m ≠ 1, as the relationship is nonproportional.
Let's test the given options:
A: y = -5x + 5, with a slope of -5, is not the correct equation as m ≠ 1.
B: y = -x + 5, with a slope of -1, is not the correct equation as m ≠ 1.
C: y = x + 5 fits the criteria as it has a slope of 1.
D: (1/5)x + 5, with a slope of 1/5, is not the correct equation as m ≠ 1.
Therefore, the linear equation that represents the nonproportional linear relationship is: C: y = x + 5
Graph the equation x−y=6 using the form y=mx+b .
To graph the equation x - y = 6 in the form y = mx + b, we first need to solve for y to get it in slope-intercept form.
Starting with the original equation:
x - y = 6
Subtract x from both sides:
-y = -x + 6
Divide by -1 to solve for y:
y = x - 6
Now we have the equation in the form y = mx + b, where the slope (m) is 1 and the y-intercept (b) is -6.
To graph the line:
1. Plot the y-intercept, which is -6 on the y-axis.
2. Use the slope, which is 1, to find another point on the line. Since the slope is 1 (which can also be written as 1/1), we can go up 1 unit and right 1 unit from the y-intercept to find another point.
3. Draw a straight line through the two points to represent the graph of the equation x - y = 6.
The graph will show a line where the slope is 1 and the y-intercept is -6.
Graph the equation x−y=6 using the form y=mx+b .
A: (0, -6), (1,-5)
B: (0,3), (3,2)
C: (0,0), (6,6)
D: (0,-4), (1,-10)
To graph the equation x - y = 6, we can rewrite it in the form y = mx + b. Let's solve for y:
x - y = 6
y = x - 6
Now we have the equation in slope-intercept form, where the slope (m) is 1 and the y-intercept (b) is -6.
Now, let's identify which set of points is consistent with the equation y = x - 6:
Check the points given in the answer choices:
A: (0, -6), (1, -5)
B: (0, 3), (3, 2)
C: (0, 0), (6, 6)
D: (0, -4), (1, -10)
By substituting the x and y coordinates of each set of points into the equation y = x - 6, we can see which set satisfies the equation:
For points A:
(0, -6) => -6 = 0 - 6 (False)
(1, -5) => -5 = 1 - 6 (True)
Therefore, the correct set of points that represents the graph of the equation x - y = 6 is A: (0, -6), (1, -5).