Page 139 - Math Course 3 (Book 1)

Equations with Slope and Points on the Line

Write an Equation Given Two Points
Your Turn!
Example Write an Equation Given Slope and One Point

The table of ordered pairs shows the coordinates of Write an equation of a line that passes through
two points on the graph of a function. (1, 4) and has a slope of –3.

Which equation describes the function? A. y = –3x + 4
B. y = –3x + 1
A. 5y = 12x – 16 x y C. y = –3x + 13
B. y = 4x – 16 D. y = –3x + 7
C. y = –4x + 16 –3 –4
D. y = –4x – 16 –2 –8

Read the Test Item Answer
The table represents the ordered pairs (–3, –4) and
(–2, –8).

Solve the Test Item
Step 1 Find the slope of the line containing the
points.
y – y
2
m = x – x 1 Slope formula
2 1
–8–(–4) Let (x , y ) = (–3, –4)
m = 1 1
–2–(–3) and (x , y ) = (–2, –8). Write an Equation Given Two Points
2
2
–4
m = or –4 Simplify. The table of ordered pairs shows the coordinates
1
of two points on the graph of a function. Which
Step 2 Use the slope and one of the two points to equation describes the function?
find the y-intercept. In this case, we chose x y
(–3, –4). A. y = –x + 4
B. y = x + 4 –1 3
y = mx + b Slope-intercept form C. y = x – 4
D. y = –x – 4 2 6
–4 = –4(–3) + b Replace m with –4,x
with –3, and y with –4.

–4 = 12 + b Multiply. Answer

–4–12 = 12 + b – 12 Subtract 12 from each side.

–16 = b Simplify.

Step 3 Write the slope-intercept form
using m = –4 and b = –16.

y = mx + b Slope-intercept form

y = –4x – 16 Replace m with –4, and
b with –16.

Answer The answer is D.

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