1. Slope, Intercepts, Rates of Change
Slope is the measure of the steepness of a line. It describes the rate of change between the coordinates of the line.

2. Slope, Intercepts, Rates of Change
Slope is the measure of the steepness of a line. It describes the rate of change between the coordinates of the line.
We will use this equation to calculate slope given two coordinates…
𝑚= 𝑦 2 − 𝑦 1 𝑥 1 − 𝑥 2 *** slope is always 𝑦 𝑥

3. Slope, Intercepts, Rates of Change
Slope is the measure of the steepness of a line. It describes the rate of change between the coordinates of the line.
We will use this equation to calculate slope given two coordinates…
𝑚= 𝑦 2 − 𝑦 1 𝑥 1 − 𝑥 2 *** slope is always 𝑦 𝑥
EXAMPLE : Find the slope between the points −2 , 4 , ( 3 , 7)

4. Slope, Intercepts, Rates of Change
Slope is the measure of the steepness of a line. It describes the rate of change between the coordinates of the line.
We will use this equation to calculate slope given two coordinates…
𝑚= 𝑦 2 − 𝑦 1 𝑥 1 − 𝑥 2 *** slope is always 𝑦 𝑥
EXAMPLE : Find the slope between the points −2 , 4 , ( 3 , 7)
𝑚= 𝑦 2 − 𝑦 1 𝑥 1 − 𝑥 2 = 7−4 3−(−2)
𝑥 1
𝑦 1
𝑥 2
𝑦 2

5. Slope, Intercepts, Rates of Change
Slope is the measure of the steepness of a line. It describes the rate of change between the coordinates of the line.
We will use this equation to calculate slope given two coordinates…
𝑚= 𝑦 2 − 𝑦 1 𝑥 1 − 𝑥 2 *** slope is always 𝑦 𝑥
EXAMPLE : Find the slope between the points −2 , 4 , ( 3 , 7)
𝑚= 𝑦 2 − 𝑦 1 𝑥 1 − 𝑥 2 = 7−4 3−(−2) = 3 5
𝑥 1
𝑦 1
𝑥 2
𝑦 2

6. Slope, Intercepts, Rates of Change
Slope is the measure of the steepness of a line. It describes the rate of change between the coordinates of the line.
We will use this equation to calculate slope given two coordinates…
𝑚= 𝑦 2 − 𝑦 1 𝑥 1 − 𝑥 2 *** slope is always 𝑦 𝑥
EXAMPLE : Find the slope between the points −2 , 4 , ( 3 , 7)
𝑚= 𝑦 2 − 𝑦 1 𝑥 1 − 𝑥 2 = 7−4 3−(−2) = 3 5
EXAMPLE #2 : Find the slope between the points 3 , −1 , ( −3 , 0 )
𝑥 1
𝑦 1
𝑥 2
𝑦 2

7. Slope, Intercepts, Rates of Change
Slope is the measure of the steepness of a line. It describes the rate of change between the coordinates of the line.
We will use this equation to calculate slope given two coordinates…
𝑚= 𝑦 2 − 𝑦 1 𝑥 1 − 𝑥 2 *** slope is always 𝑦 𝑥
EXAMPLE : Find the slope between the points −2 , 4 , ( 3 , 7)
𝑚= 𝑦 2 − 𝑦 1 𝑥 1 − 𝑥 2 = 7−4 3−(−2) = 3 5
EXAMPLE #2 : Find the slope between the points 3 , −1 , ( −3 , 0 )
𝑚= 𝑦 2 − 𝑦 1 𝑥 1 − 𝑥 2 = 0−(−1) −3−3 = 1 − 𝑂𝑅 −1 6
𝑥 1
𝑦 1
𝑥 2
𝑦 2

8. Slope, Intercepts, Rates of Change
When a graph of the line is shown, you can simply “count” the slope. Starting at one point, count the vertical and horizontal change to another point. Up and down moves correspond with your y – value, left and right moves correspond to your x – value. +𝒚 −𝒙 +𝒙 −𝒚

9. Slope, Intercepts, Rates of Change
When a graph of the line is shown, you can simply “count” the slope. Starting at one point, count the vertical and horizontal change to another point. Up and down moves correspond with your y – value, left and right moves correspond to your x – value. +𝒚
Choose two points that are easily identified… −𝒙 +𝒙 −𝒚

10. Slope, Intercepts, Rates of Change
When a graph of the line is shown, you can simply “count” the slope. Starting at one point, count the vertical and horizontal change to another point. Up and down moves correspond with your y – value, left and right moves correspond to your x – value. +𝒚
Choose two points that are easily identified…
Start with one of the points and start counting your vertical and horizontal changes… −𝒙 +𝒙 −𝟑 +𝟐 −𝒚

11. Slope, Intercepts, Rates of Change
When a graph of the line is shown, you can simply “count” the slope. Starting at one point, count the vertical and horizontal change to another point. Up and down moves correspond with your y – value, left and right moves correspond to your x – value. +𝒚
Choose two points that are easily identified…
Start with one of the points and start counting your vertical and horizontal changes…
The slope of this line is
𝑚= −3 2 −𝒙 +𝒙 −𝟑 +𝟐 −𝒚

12. Slope, Intercepts, Rates of Change
Given this situation, you can also identify the coordinates and use the previous formula… +𝒚
𝑚= 𝑦 2 − 𝑦 1 𝑥 1 − 𝑥 2 = −2−(−5) 2−4 = 3 −2 −𝒙 +𝒙
2 , −2
4 , −5 −𝒚

13. Slope, Intercepts, Rates of Change
Some special slope values…
Horizontal lines have a slope of zero. This is due to the fact the y – values for all coordinates of the line are equal. +𝒚
𝑚= 𝑦 2 − 𝑦 1 𝑥 1 − 𝑥 2 = 3−3 −3−4 = 0 −7 =0
−3 , 3
4 , 3 −𝒙 +𝒙 −𝒚

14. Slope, Intercepts, Rates of Change
Some special slope values…
Vertical lines have an undefined or no slope. This is due to the fact the x – values for all coordinates of the line are equal. +𝒚
𝑚= 𝑦 2 − 𝑦 1 𝑥 1 − 𝑥 2 = 1−(−4) 2−2 = 5 0
2, 1 −𝒙 +𝒙
2 , −4 −𝒚

15. Slope, Intercepts, Rates of Change
Intercepts of a line occur on both the x and y axis. We will simply identify where the line “cuts” through the axis.
X – intercepts have a y – value of zero
Y – intercepts have an x – value of zero

16. Slope, Intercepts, Rates of Change
Intercepts of a line occur on both the x and y axis. We will simply identify where the line “cuts” through the axis.
X – intercepts have a y – value of zero
Y – intercepts have an x – value of zero +𝒚
y – intercept = ( 6 , 0 ) −𝒙 +𝒙 −𝒚

17. Slope, Intercepts, Rates of Change
Intercepts of a line occur on both the x and y axis. We will simply identify where the line “cuts” through the axis.
X – intercepts have a y – value of zero
Y – intercepts have an x – value of zero +𝒚
y – intercept = ( 6 , 0 )
x – intercept = ( 0 , −3 ) −𝒙 +𝒙 −𝒚

18. Slope, Intercepts, Rates of Change
Rates of change show the relationship between two quantities that are changing. The change can be constant or vary. Linear equations have a rate of change that is constant and it is the slope.

19. Slope, Intercepts, Rates of Change
Rates of change show the relationship between two quantities that are changing. The change can be constant or vary. Linear equations have a rate of change that is constant and it is the slope.
EXAMPLE : Grant is tracking the growth of his newly planted tree. In 2 months the tree has grown to 3 feet. In 8 months, the tree has grown to 6 feet. What is the rate of change of growth for Grant’s tree ?

20. Slope, Intercepts, Rates of Change
Rates of change show the relationship between two quantities that are changing. The change can be constant or vary. Linear equations have a rate of change that is constant and it is the slope.
EXAMPLE : Grant is tracking the growth of his newly planted tree. In 2 months the tree has grown to 3 feet. In 8 months, the tree has grown to 6 feet. What is the rate of change of growth for Grant’s tree ?
Using the data as coordinates 2 , 3 , ( 8 , 6 )…
𝑚= 6−3 8−2 = 3 6 = 1 2
Grant’s tree grows 1 foot in every 2 months as a rate of change.