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How to Write a Linear Equation in Y = Form
Example 1 Write an Equation Given Slope and One Point
Write an equation of a line that passes through (-1, 2) with a slope of
Step 1 Find the y -intercept by replacing m with
and ( x , y ) with (-1, 2) in the slope-intercept form
and solving for b. y = mx + b Slope-intercept form
2 =
(-1) + b Replace m with
, y with 2, and x with – 1.
Add
to each side.
= b Simplify.
Step 2 Write the slope-intercept form using m =
and b = 2
or
y = mx + b Slope-intercept form
y =
x +
Replace m with
and b with
.
Therefore, the equation is y =
x +
Check: You can check your result by graphing y =
x +
on a graphing calculator. Use the CALC
menu to verify.
Example 2 Write an Equation Given Two Points
Standardized Test Practice The table of ordered pairs shows the coordinates of two points on the graph of a function. Which equation describes the function? x y
A. y = -4 x +1 B. y =
x + 1
C. y = 4 x + 1 D. y = -
x – 1
Read the Test Item The table represents the ordered pairs (-2, -7) and (1, 5).
Solve the Test Item Step 1 Find the slope of the line containing the points.
m = 2 1
2 1
x x
y y
Slope formula
m =
Let ( x (^) 1 , y (^) 1 ) = (-2, -7) and ( x (^) 2 , y (^) 2 ) = (1, 5).
m =
or 4 Simplify.
Step 2 Use the slope and one of the two points to find the y -intercept. y = mx + b Slope-intercept form 5 = 4(1) + b Let ( x , y ) = (1, 5); replace m with 4. 5 = 4 + b Multiply. 5 – 4 = 4 + b – 4 Subtract 4 from each side. 1 = b Simplify.
Step 3 Write the slope-intercept form using m = 4 and b = 1. y = mx + b Slope-intercept form y = 4 x + 1 Replace m with 4 and b with 1.
The answer is C.
