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2.3 Writing Equations of Lines

In this section you will learn to

• use point-slope form to write an equation of a line

• use slope-intercept form to write an equation of a line

• graph linear equations using the slope and y-intercept

• find the slopes and equations of parallel and perpendicular lines

• recognize and use the standard form of a line

Point-Slope Form

Slope-Intercept Form

The point-slope form of the equation of a nonvertical

The slope-intercept form of the equation of a

nonvertical line with slope m and y-intercept b is

line with slope m that passes through

(

,

)

is

x

y

1

1

=

+

y

mx

b

(

)

y

−

y

=

m

x

−

x

1

1

Example 1: Find an equation for the line that passes through the point (-2, 7) and has a slope equal to -5.

Write the equation in point-slope form. Then write the equation in slope-intercept form. (Solve for y.)

Steps:

1. Substitute

,

,

and m values.

x

y

1

1

2. Simplify and solve for y.

3. Check given point and slope (m).

Example 2: Find an equation for the line passing through the points (6, -8) and (4, -3). Write your

equation in point-slope form and then in slope-intercept form.

Steps:

1. Find the slope.

2. Substitute the slope and the

values for one of the points.

3. Simplify and solve for y.

4. Check the point and slope.

Page 1 (Section 2.3)

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