What is the equation of the line that passes through the points (15, 9) and (-2, 9)?
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Since both points have the same y-coordinate, the line is a horizontal line. The equation of a horizontal line is y = b, where b is the y-coordinate. In this case, b = 9, so the equation of the line is y = 9.
What are the slope and the y-intercept of the linear function that is represented by the graph?
On a coordinate plane, a line goes through points (negative 3, 0) and (negative 2, 4).
The slope is 3, and the y-intercept is 9.
The slope is 3, and the y-intercept is 12.
The slope is 4, and the y-intercept is 9.
The slope is 4, and the y-intercept is 12.
The slope of a line can be found using the formula m = (y2 - y1)/(x2 - x1), where (x1, y1) and (x2, y2) are any two points on the line. Using the given points, we have:
m = (4 - 0)/(-2 - (-3)) = 4/1 = 4
Therefore, the slope of the linear function is 4.
To find the y-intercept, we can use the point-slope form of a linear equation: y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope. Using the point (−3, 0) and the slope 4, we have:
y - 0 = 4(x - (-3))
y = 4x + 12
Therefore, the y-intercept is 12.
The answer is: The slope is 4, and the y-intercept is 12.
A linear function has a slope of Negative StartFraction 7 Over 9 EndFraction and a y-intercept of 3. How does this function compare to the linear function that is represented by the equation y + 11 = Negative StartFraction 7 Over 9 EndFraction (x minus 18)?
It has the same slope and the same y-intercept.
It has the same slope and a different y-intercept.
It has the same y-intercept and a different slope.
It has a different slope and a different y-intercept.
The linear function with a slope of Negative StartFraction 7 Over 9 EndFraction and a y-intercept of 3 can be written as y = Negative StartFraction 7 Over 9 EndFraction x + 3.
The linear function represented by the equation y + 11 = Negative StartFraction 7 Over 9 EndFraction (x minus 18) can be rewritten in slope-intercept form as y = Negative StartFraction 7 Over 9 EndFraction x + 11 + Negative StartFraction 7 Over 9 EndFraction (18) = Negative StartFraction 7 Over 9 EndFraction x + 25.
Comparing the two functions, we see that they have the same slope, Negative StartFraction 7 Over 9 EndFraction, but different y-intercepts: 3 for the first function, and 25 for the second function.
Therefore, the answer is: It has the same slope and a different y-intercept.
What can be concluded about the line represented in the table? Select 3 options.
x
y
–6
–7
2
–3
8
0
The slope is 2.
The slope is One-half.
The y-intercept is –4.
The y-intercept is 8.
The points (–2, –5) and (8, 0) are also on the line.
The points (–5, –2) and (1, 10) are also on the line.
From the given table, we can calculate the slope (m) of the line by using any two points. Using (–6, –7) and (2, –3), we get:
m = (y2 - y1)/(x2 - x1) = (-3 - (-7))/(2 - (-6)) = 4/8 = 1/2
Therefore, option 2, "The slope is One-half," is correct.
We can also calculate the y-intercept (b) of the line by using any point and the slope. Using the point (2, –3) and the slope 1/2, we get:
y - y1 = m(x - x1)
y - (-3) = 1/2(x - 2)
y = 1/2x - 2 + (-3)
y = 1/2x - 5
Therefore, option 3, "The y-intercept is –4," is incorrect, and option 4, "The y-intercept is 8," is also incorrect.
To check whether the points (–2, –5) and (8, 0) are on the line, we can substitute their x and y values into the equation of the line and see if they satisfy it.
For (-2, -5):
y = 1/2x - 5
y = 1/2(-2) - 5
y = -6
The point (-2, -5) does not lie on the line. So, option 5 is incorrect.
For (8, 0):
y = 1/2x - 5
y = 1/2(8) - 5
y = -1
The point (8, 0) does not lie on the line. So, option 5 is also incorrect.
Therefore, the only correct option is:
The slope is One-half.
The graph shows the amount of water that remains in a barrel after it begins to leak. The variable x represents the number of days that have passed since the barrel was filled, and y represents the number of gallons of water that remain in the barrel.
A graph titled Water Supply with number of days on the x-axis and gallons of water left on the y-axis. A line goes through points (6, 33) and (15, 15).
What does the y-intercept represent?
the amount of water that is added to the barrel each day
the amount of water that remains in the water barrel
the amount of water that is initially in the water barrel
the amount that the water barrel decreases each day
The y-intercept of the line is the value of y when x is equal to 0. In this case, we are not given the value of y when x is equal to 0, since the line only goes through the points (6, 33) and (15, 15).
Therefore, we cannot determine what the y-intercept represents based on the information given in the graph.
Option 1, "the amount of water that is added to the barrel each day," is incorrect, as the graph does not provide any information about water being added to the barrel.
Option 2, "the amount of water that remains in the water barrel," is also incorrect, as we have already established that the y-intercept cannot be determined from the given information.
Option 3, "the amount of water that is initially in the water barrel," is a possibility, as the y-intercept could represent the initial amount of water in the barrel before any days have passed. However, we cannot confirm this without knowing the value of y when x is equal to 0.
Option 4, "the amount that the water barrel decreases each day," is also incorrect, as the line in the graph shows the amount of water remaining in the barrel, not the amount by which it is decreasing each day.
Therefore, the answer is: Not enough information is given to determine what the y-intercept represents.
The slope of the graph of the equation y = 2 x minus 2 is 2. What is the y-intercept?
y-intercept =