1. Slope is the steepness of a line.
What does the 7% mean? 7%
7% is the slope of the road. It means the road drops 7 feet vertically for every 100 feet horizontally.
7 feet
100 feet
So, what is slope???
Slope is the steepness of a line.

2. Slopes of Lines
A line with positive slope slants upward from left to right.
A line with negative slope slants downward from left to right.
A line with slope of 0 is horizontal.
A line with an undefined slope is vertical.

3. Slope can be expressed different ways:
A line has a positive slope if it is going uphill from left to right.
A line has a negative slope if it is
going downhill from left to right.

4. Determine the slope of the line.
Start with the lower point and count how much you rise and run to get to the other point!
rise 3 = =
run 6 6 3
Notice the slope is positive AND the line increases!

5. Determine the slope of the line.-1
Find points on the graph.
Use two of them and apply rise over run. 2
The line is decreasing (slope is negative).

6. Writing Linear Equations
Linear Equation – an equation whose graph is a line. Examples:
Y-Intercept the y-coordinate of the point where a line crosses the y- axis.

7. Slope Intercept Form of a Linear Equation
y = mx + b
slope y-intercept
What are the slope and y-intercept of y = 3x – 5 ?
the slope is 3, and the y-intercept is -5
What are the slope and y-intercept of y=-2x + 1?
the slope is -2, and the y-intercept is 1

8. Graphing Linear Equations
Each point on the graph of an equation is an ordered pair that makes the equation true. The graph of a linear equation is a line that indicates all the solutions of the equation. You can use the slope and y-intercept to graph a line.

9. y = 2x + 1 Now look at the graph of the line.
Step 1: Look at the y-intercept and plot
where the graphs cross the “y” axis.
Step 2: Use the slope (rise/run) to determine the next point and plot. Remember that the slope is 2, so go up 2 and to the right 1.
Step 3: Draw a line through both points. Be sure to extend pass point and put arrow at both ends.

10. y = -2x + 3 Now look at the graph of the line.
Step 1: Look at the y-intercept and plot
where the graphs cross the “y” axis.
Step 2: Use the slope (rise/run) to determine the next point and plot. Remember that the slope is -2/1. So go down 2, and to the right 1.
Step 3: Draw a line through both points. Be sure to extend pass point and put arrow at both ends.

11. Find the slope of the line that passes through the points (-2, -2) and (4, 1).
When given points, it is easier to use the formula!
y2 is the y coordinate of the 2nd ordered pair (y2 = 1)
y1 is the y coordinate of the 1st ordered pair (y1 = -2)

12. Find the slope of the line that passes through (3, 5) and (-1, 4).-4
- ¼

13. Point-Slope Form (x1 ,y1) m = rise = slope point run
y – y1 = m(x – x1)
(x1 ,y1) m = rise = slope
point run

14. Writing in Point-Slope
Given a point and a slope, write an equation in point- slope form
y – y1 = m(x – x1)
Example 1: (3,8) m = 2
y – 8 = 2 (x – 3)
x1, y1