Easy Algebra Step-by-Step

192 Easy Algebra Step-by-Step

Determining the Equation of a Line Given Two Distinct Points on the Line

You also use the point-slope equation with this method.

Problem Given the points (3, 4) and (1, 2) on the line, write the

equation of the line.

Solution

Step 1. Use the two points to determine the slope using the point-slope

equation.

m= ==

42 −

31 −

2

2

1

Step 2. Now use the point-slope formula and one of the given points to fi nish

writing the equation. Let (x, y) be a point on the line different from,

say, (3, 4).

y

x

−

−

=

4

3

1

Step 3. Solve the equation for y to get the slope-y-intercept form of the

equation.

y

x

−

−

=

4

3

1

y − 4 = x − 3

y − 4 + 4 =x − 3 + 4

y = x + 1 is the equation of the line.

Problem Given the points (−1, 4) and (3, −7) on the line, write the equa-

tion of the line.

Solution

Step 1. Use the two points to determine the slope using the point-slope

equation.

m=

()

()−

=

−

=−

4 −(−

)− 3

47 +

4

11

4