Page 110 - Math Course 3 (Book 1)

Writing Linear Equations

Write an equation in slope-intercept form for the line Write an Equation From a Table
graphed.
Examples

Use the table of values to write an x y
equation in slope-intercept form.
–2 16
Step 1 Find the slope m. Use the –1 10
coordinates of any two points.
0 4

y = mx + b Slope-intercept form m = y – y 1 Definition of slope 1 –2
2
x – x
2
1
y = 1x + (–4) Replace m with 1 and b 10 –16 (x , y ) = (–2, 16)
with –4. = –1–(–2) (x , y ) = (–1, 10)
1
1
2 2
y = x – 4 Simplify. = –6 or –6
1
Answer y = x – 4 Step 2 Find the y-intercept b.
Use the slope and the coordinates of either point.

y = mx + b Slope-intercept form
Write an Equation Given Two Points
16 = –6(–2) + b Replace (x, y) with
Examples (–2, 16) and m with –6.

4 = b Simplify.
Write an equation for the line that passes through
(7, 0) and (6, 3).
Step 3 Substitute the slope and y-intercept.
Step 1 Find the slope m.
y = mx + b Slope-intercept form
y – y
2
m = x – x 1 Definition of slope y = –6x + 4 Replace m with –6 and b with 4.
2 1
3 – 0 (x , y ) = (7, 0)
= 1 1
6 – 7 (x , y ) = (6, 3) Answer y = –6x + 4
2 2
= 3 or –3
–1
Step 2 Find the y-intercept b. Use the slope Your Turn!
and the coordinates of either point.
Write an Equation From a Graph
y = mx + b Slope-intercept form
Write an equation in slope-intercept form for the
0 = –3(7) + b Replace (x, y) with (7, 0) and m line graphed.
with –3. 2
A. y = – x + 3
5
21 = b Simplify. 2
B. y = x + 3
Step 3 Substitute the slope and y-intercept 5
2
C. x + y = 3
y = mx + b Slope-intercept form 5
D. y = 3x – 2
y = –3x + 21 Replace m with –3 and b with 21. 5

Answer y = –3x + 21 Answer

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