Easy Algebra Step-by-Step

190 Easy Algebra Step-by-Step

Problem Given the slope m=

1

2

and the y-intercept y= −2, write the

equation of the line.

Solution

Step 1. Recalling that the slope-y-intercept form of the equation of a line is

ymmmmmxbx , write the equation.

The equation of the line is yxx−

1

2

2.

Determining the Equation of a Line Given the Slope and One Point on the Line

For this method, you use the point-slope equation

m

yy

xx

=^2

y

12 x

, where (x 1 , y 1 ) and (x 2 , y 2 ) are points on the

line.

Problem Given the slope m = 2 and a point (3, 2) on the line, write the

equation of the line.

Solution

Step 1. Let (x, y) be a point on the line different from (3, 2), then substitute

the given information into the point-slope formula: m

yy

xx

=^2

y

12 x

.

2

2

3

=

−

−

y

x

Step 2. Solve the equation for y to get the slope-y-intercept form of the

equation.

2

2

3

=

−

−

y

x

2(x − 3) = y − 2

2 x − 6 = y − 2

2 x − 6 + 2 = y − 2 + 2

2 x − 4 = y

y = 2 x − 4 is the equation of the line.

Watch your signs when you

use the point-slope equation.