The Algebra Teacher\'s Guide to Reteaching Essential Concepts and Skills

Name Date

WORKSHEET 4.13: WRITING A LINEAR EQUATION,

GIVEN TWO POINTS

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Follow the steps below to write an equation from two points on a graph:

1. Find the slope of the line. Use the equationm=

y 2 −y 1

x 2 −x 1

.

2. Find they-intercept. Use the equationy=mx+b.Replacemwith the slope of the line.
   Replacexandywith the values from one of the given ordered pairs. Solve forb.


3. Write the equation of the line using slope-intercept form. Substitute the slope,m,and
   they-intercept,b, into slope-intercept form,y=mx+b.

EXAMPLE

Write an equation of the line that passes through the points (3, 1) and (6, 7).

Find the slope of the line:m=

7 − 1

6 − 3

=

6

3

= 2. The slope of the line is 2.

Find they-intercept: 1 = 2 (3)+bor 1= 6 +b.They-intercept is−5.

The equation of the line isy= 2 x− 5.

DIRECTIONS: Write an equation in slope-intercept form of the line that passes through

the points.

1. (1, 9), (2, 13) 2. (5,−7), (3,−3)


2. (3, 5), (−2,−20) 4.(1,−3), (−1,−1)

5.(2, 5), (8, 8) 6.(3,−1), (9, 3)

7.(12, 3), (−4, 7) 8.(2, 3), (4,−11)

CHALLENGE:Bob found the equation of the line that contains points (1, 1) and

(5, 5) to bey=x. Jim said that the equation for this line should be written

asy=x+0because0isthey-intercept. Who is correct? Explain.

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2011 by Judith A. Muschla, Gary Robert Muschla, and Erin Muschla. All rights reserved.