A construction worker built steps up to a
home. The table shows the linear relationship
between the height off the ground in inches
and the number of steps.
Number of Steps Height (inches)
3 20
5 36
7 52
9 68
11 84
What is the rate of change of height off the
ground with respect to the number of steps?
8in. per step
16in. per step
8
1
in. per step
16
1
in. per step
The rate of change of height off the ground with respect to the number of steps can be calculated by finding the difference in height for each step and dividing it by the number of steps.
For example, between 3 steps and 5 steps, the height difference is 36 - 20 = 16 inches. The number of steps is 5 - 3 = 2 steps. Therefore, the rate of change is 16 inches / 2 steps = 8 inches per step.
Similarly, for the rest of the data points:
- Between 5 steps and 7 steps: height difference = 52 - 36 = 16 inches, number of steps = 7 - 5 = 2 steps, rate of change = 16 inches / 2 steps = 8 inches per step.
- Between 7 steps and 9 steps: height difference = 68 - 52 = 16 inches, number of steps = 9 - 7 = 2 steps, rate of change = 16 inches / 2 steps = 8 inches per step.
- Between 9 steps and 11 steps: height difference = 84 - 68 = 16 inches, number of steps = 11 - 9 = 2 steps, rate of change = 16 inches / 2 steps = 8 inches per step.
Therefore, the rate of change of height off the ground with respect to the number of steps is 8 inches per step.
The graph of a line is shown on the grid. The
coordinates of both points indicated on the
graph of the line are integers.
What is the rate of change of with respect to
for this line?
y
x
7
3
3
2
− 5
7
− 7
5
To find the rate of change with respect to x for this line, we need to calculate the difference in y-coordinates and divide it by the difference in x-coordinates.
Given the coordinates of the two points indicated on the graph:
Point A: (3, 7)
Point B: (2, -5)
The difference in y-coordinates is: -5 - 7 = -12
The difference in x-coordinates is: 2 - 3 = -1
To find the rate of change with respect to x, we divide the difference in y-coordinates by the difference in x-coordinates:
rate of change = -12 / -1 = 12
Therefore, the rate of change of y with respect to x for this line is 12.
The graph of a linear function is shown on the
grid.
What are the -intercept and the -intercept
of the line?
x y
x-intercept: (6,0)
y-intercept: (0,−3)
x-intercept: (0,6)
y-intercept: (−3,0)
x-intercept: (−3,0)
y-intercept: (0,6)
x-intercept: (0,−3)
y-intercept: (6,0)
The x-intercept is the point at which the line intersects the x-axis, meaning the y-coordinate is 0. So, the x-intercept is (6, 0).
The y-intercept is the point at which the line intersects the y-axis, meaning the x-coordinate is 0. So, the y-intercept is (0, -3).
Therefore, the x-intercept is (6, 0) and the y-intercept is (0, -3).