1. Graphing and Writing Equations of Lines (2-4)
Objective: Graph linear equations and write the equations of lines in slope-intercept and point-slope form.

2. Forms of Linear Equations
There are three main forms for the equation of a line
Slope-Intercept Form y = mx + b
m = slope
b = y-intercept
Standard Form Ax + By = C
A, B and C integers
A > 0, A and B not both 0
Point-Slope Form y - y1 = m(x – x1)
(x1, y1) is any point on the line

3. Graphing Lines From slope intercept form
Determine the y-intercept and plot it on the graph FIRST
Determine the slope and use it to find one or more additional points
Connect the points. Don’t forget to put arrows on the ends.

4. Graphing Lines Example: Graph Graph the y-intercept of -5
From the y-intercept, use the slope to rise 2 and run 3. This will give you a second point. Repeat.
Use a ruler to connect the points and create a line. . . .

5. Graphing Lines From Standard Form
Method 1: convert to slope-intercept form
Method 2: find x- and y-intercepts

6. Graphing Lines Graph 3x + 4y = 24 x – intercept y-intercept.
.0.

7. Graphing Lines From point-slope form Determine the point (x1, y1)
Graph the point
Use the slope to find additional points
Draw the line

8. Graphing Lines Graph y – 5 = -2(x + 1) Rewrite as y – 5 = -2(x - -1)
The point is (-1, 5)
Graph the point
The slope is -2/1, so rise -2 and run 1 .

9. Writing Equations of Lines
You must be given two pieces of information to write the equation of a line. This information can be
Slope and y-intercept
Slope and one point
Two points
If you are given the graph of a line, you can get that information from the graph.

10. Writing Equations of Lines
b = -1
y = mx + b
b = -1 -1
y = ___x + ___
rise = -2
run = 3

11. Writing Equations of Lines
Write the equation of a line with slope -3 and one point at (-5, 2)
When given the slope and one point, it is easiest to use the point-slope form
y – y1 = m(x – x1)
y – 2 = -3(x - -5)
y – 2 = -3(x + 5) covert to slope-intercept
y – 2 = -3x – 15
y = -3x - 13

12. Writing Equations of Lines
When given two points you need to:
Use the slope formula to determine the slope
Use the calculated slope and one of the two points to determine the equation of the line

13. Writing Equations of Lines
Write the equation of the line passing through (-3, 5) and (6, -2).
Find the slope
Use the slope and one of the two points to write the equation
y – y1 = m(x – x1)

14. Parallel and Perpendicular Lines
Parallel lines have the SAME slope
Perpendicular lines have slopes that are OPPOSITE RECIPROCALS

15. Parallel and Perpendicular Lines
Find the equation of the line parallel to x + 5y = 7 and passing through (10, -2)
Find the slope of the original line:
From standard form, slope is –A/B
The slope of the line above is -3/5, so the slope of the parallel line is also -3/5
Use the slope and the point to write the equation

16. Parallel and Perpendicular Lines
Find the equation of the line perpendicular to 8x – 2y = 9 and with y-intercept -4
Find the slope of the line: -A/B = -8/-2 = 4
The slope of the line perpendicular to the given line would be
Use the slope and the y-intercept to write the equation of the line