Chapter 4 Graphing And Writing Linear Equations - Section 4.7 Writing Equations In Point-Slope Form Worksheet Page 4
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1
2
3
4
5
6Writing an Equation Using Two Points
2 2
EXAMPLE
Write in slope-intercept form an equation of the line that passes
through the points (2, 4) and (5, −2).
Study Tip
− y
y
−2 − 4
− 6
Find the slope: m =
=
=
= − 2
2
1
—
—
—
− x
5 − 2
You can use either of
x
3
2
1
the given points to
Then use the slope m = −2 and the point (2, 4) to write an
write the equation of
equation of the line.
the line.
Use m = − 2 and
y −
= m(x −
y
x
)
Write the point-slope form.
(5, − 2).
1
1
y − (− 2) = − 2(x − 5)
y −
=
−
2(x − 2)
Substitute −2 for m, 2 for x
4
, and 4 for y
.
1
1
y + 2 = − 2x + 10
✓
y − 4 = − 2x + 4
Distributive Property
y = − 2x + 8
y = − 2x + 8
Write in slope-intercept form.
Real-Life Application
3 3
EXAMPLE
You fi nish parasailing and are being pulled back to the boat. After
2 seconds, you are 25 feet above the boat. (a) Write and graph an
equation that represents your height y (in feet) above the boat after
x seconds. (b) At what height were you parasailing?
a. You are being pulled down at the rate of 10 feet per second.
So, the slope is −10. You are 25 feet above the boat after 2 seconds.
So, the line passes through (2, 25). Use the point-slope form.
y −
= −10(x − 2)
25
Substitute for m, x
, and y
.
1
1
10 feet
y − 25 = −10x + 20
Distributive Property
per
second
y = −10x + 45
Write in slope-intercept form.
y
So, the equation is y = −10x + 45.
45
y
10x
45
40
b. You start descending when x = 0. The
35
y-intercept is 45. So, you were parasailing
30
(2, 25)
25
at a height of 45 feet.
20
15
10
5
0
0
1
2
3
4
5
6
7
x
Write in slope-intercept form an equation of the line that passes
through the given points.
Exercises 12 – 17
4. (− 2, 1), (3, − 4)
5. (− 5, − 5), (− 3, 3)
6. (− 8, 6), (− 2, 9)
7.
WHAT IF?
In Example 3, you are 35 feet above the boat after
2 seconds. Write and graph an equation that represents your
height y (in feet) above the boat after x seconds.
Section 4.7
Writing Equations in Point-Slope Form
187
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