When you are given two points, but do not know the
y-intercept, you should first use the point-slope form to write the equation of the
line that passes through the points, as in Example 2.
POINT-SLOPE FORM
EXAMPLE
Write an Equation of a Line Given Two Points
2
Write in slope-intercept form the equation of the line that passes through the
points (3, 2) and (6, 0).
Solution
Find the slope. Use (x1, y1) (3, 2) and (x2, y2 ) (6, 0).
y2 y1
Write formula for slope.
m
x2 x1
0 (2)
63
Substitute.
2
3
Simplify.
Write the equation of the line. Use point-slope form, because you do not
know the y-intercept.
y y1 m(x x1)
2
3
Substitute for m, 3 for x1, 2 for y1.
2
3
Simplify and use distributive property.
2
3
Subtract 2 from each side.
y (2) (x 3)
y 2 x 2
y x 4
ANSWER 䊳
CHECK
Write point-slope form.
2
3
2
3
The equation of the line is y x 4.
✓
You can check your
answer by graphing.
y
1
Notice that the graph of
1
1
2
3
y x 4 passes
through (3, 2) and (6, 0).
You can also check your
answer using substitution.
(6, 0)
1
7 x
(3, 2)
3
5
3
(0, 4)
y 23 x 4
Write an Equation of a Line Given Two Points
Write in slope-intercept form the equation of the line that passes through
the given points. Check your answer.
2. (2, 3) and (4, 7)
286
Chapter 5
Writing Linear Equations
3. (4, 5) and (2, 2)
4. (1, 1) and (4, 4)