Easy Algebra Step-by-Step

The Equation of a Line 191

Problem Given the slope m=

1

2

and a point (−1, 3) on the line, write the

equation of the line.

Solution

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

the given information into the point-slope formula: m

yy

xx

=^2

y

12 x

.

y

x

−

−()−

=

(^31)
2
Step 2. Solve the equation for y to get the slope-y-intercept form of the equation.
y
x

−

+

=

3

1

1

2

yx 3 ()x+

1

2

yx 3 +

1

2

1

2

yx 33 + =+x +

1

2

1

2

3

yx=+x

1

2

7

2

is the equation of the line.

Problem Given the slope m= −2 and a point (0, 0) on the line, write the

equation of the line.

Solution

Step 1. Let (x, y) be a point on the line different from (0, 0), then substitute

the given information into the point-slope formula: m

yy

xx

=^2

y

12 x

.

y

x

−

−

=−

0

0

2

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

y

x

−

−

=−

0

0

2

y

x

=− 2

y = −2x is the equation of the line.