1. Lesson: 4 – 6 Equations of Lines
Applied Geometry
Lesson: 4 – 6
Equations of Lines
Objective:
Learn to write and graph equations of lines.

2. Linear Equation Any equation whose graph is a straight line. Example
y = 2x – 1

3. y = 2x - 1 m = 2 What is the slope of y = 2x – 1? y – intercept is -1
What other similarities
do you notice about
the graph and equation?
y – intercept is -1

4. Slope-Intercept Form y = mx + b y = 2x – 1 m is the slope
b is the y-intercept
y = 2x – 1
m = 2
b = -1

5. Name the slope and y-intercept of the graph of each equation.
b = 5
y = 3
x = -2
m = 0
b = 3
m = undefined
b = none

6. Name the slope and y-intercept of the graph of each equation.
2x – 3y = 18
Has to be in y = mx + b form to name
slope and y-intercept.
2x = 3y + 18
m = 2/3
b = -6
2x - 18 = 3y

7. Name the slope and y-intercept of the graph of each equation.
y = -x + 8
y = -1
x + 4y = 24
x = 10
4y = -x + 24
m = -1
b = 8
y = (-1/4)x + 6
m = -1/4
b = 6
m = 0
b = -1
m = undefined
b = none

8. Graph 2x + y = 3 using the slope and y-intercept.
Rewrite into slope-intercept form.
y = -2x + 3
Step 1: Put a dot on
y-intercept.
Step 2: Use slope to find
another point on the graph.
Step 3: Draw line.

9. Graph –x + 3y = 9
3y = x + 9
y = (1/3)x + 3

10. Write an equation of the line parallel to y = 2x – 5 that passes through the point (3, 7).
Need the slope and y-intercept.
m = 2
Fill in slope and ordered pair in y = mx + b, solve for b.
y = mx + b
Rewrite equation
with m & b
7 = 2(3) + b
1 = b
y = 2x + 1

11. y = -3x + 6 m = -3 4 = -3(1) + b 4 = -3 + b y = -3x + 7 7= b
Write an equation parallel to the graph of 3x + y = 6 that passes through the point at (1, 4).
Need the slope and y-intercept.
y = -3x + 6
m = -3
Fill in what you know y = mx + b, solve for b.
4 = -3(1) + b
Rewrite equation
with m & b
4 = -3 + b
y = -3x + 7
7= b

12. Write an equation perpendicular to the graph of y = (1/4)x + 5 that passes through the point at (-3, 8).
Need the slope and y-intercept.
m = -4 remember has to be perpendicular.
Fill in what you know y = mx + b, solve for b.
8 = -4(-3) + b
8 = 12 + b
Rewrite equation
with m & b
-4 = b
y = -4x - 4

13. Homework
Pg – 12 all, 14 – 42 EOE