1. Writing Equations of Lines

2. From a Graph IF YOU CAN TELL THE Y-INTERCEPT Determine the y-intercept
Find a “good” second point
Count the RISE and the RUN (from left to right) to find slope
Plug into Slope-Intercept form

3. From a Graph IF YOU ARE UNABLE TO DETERMINE THE Y-INTERCEPT
Find a “good” point
Find a “good” second point
Count the RISE and the RUN (from left to right) to find slope
Choose one of the points
Plug into POINT-SLOPE form and then solve for y

4. Example 1
Write the equation for the graph.
Down 1
Right 5

5. Example 2
Write the equation for the graph.
Right 10
Up 8

6. From Given Information
GIVEN the SLOPE and the Y-INTERCEPT
Take each piece of information and plug into Slope-Intercept Form
EXAMPLE 3
Write the equation of the line with slope 3 and
y-intercept (0, -5).

7. From Given Information
GIVEN a POINT and the SLOPE.
Take each piece of information and plug into Point-Slope Form. Solve for y.
EXAMPLE 4
Write the equation of the line with slope -2 that passes through the point (-4, 7).

8. From Given Information
GIVEN 2 POINTS
Find the slope using the formula:
where the points are (x1, y1) and (x2, y2)
Choose one of the points
Plug the information into the POINT-SLOPE form
Solve for y.

9. Example 5
Write the equation for the line passing through (-4, 5) and (6, -15).

10. “SPECIAL” Lines Parallel Lines have the same slope
Parallel lines never intersect.
For two lines to be parallel, they must move in the exact same direction, but be in different locations.
In other words,
have the same slope
have different y-intercepts

11. “SPECIAL” Lines PERPENDICULAR Lines
Perpendicular lines intersect at right (90o) angles.
For two lines to be perpendicular, then, one line must go up while the other must go down.
Also, the rate that a line rises/falls must be the rate that the other runs, and vice versa.
In other words, the slopes of perpendicular lines are opposite signs and reciprocals of each other.

12. Example 6
Write the equation of the line through (-2, 5) parallel to y=4x-3.

13. Example 7
Write the equation of the line through (5, 1) perpendicular to