Equations Of Lines In Slope-Intercept And Standard Form Worksheet Page 5
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4.3 Equations of Lines in Slope-Intercept and Standard Form
Applications
The slope-intercept and standard forms are both important in applications.
E X A M P L E
7
Changing forms
A landscaper has a total of $800 to spend on bushes at $20 each and trees at $50
each. So if x is the number of bushes and y is the number of trees he can buy, then
20x
50y
800. Write this equation in slope-intercept form. Find and interpret
the y-intercept and the slope.
Solution
Write in slope-intercept form:
20x
50y
800
50y
20x
800
2
y
x
16
5
2
The slope is
and the intercept is (0, 16). So he can get 16 trees if he buys no
5
I
2
bushes and he loses
of a tree for each additional bush that he purchases.
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W A R M - U P S
True or false? Explain your answer.
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1. There is only one line with y-intercept (0, 3) and slope
.
3
2. The equation of the line through (1, 2) with slope 3 is y
3x
2.
3. The vertical line x
2 has no y-intercept.
4. The equation x
5 has a graph that is a vertical line.
5. The line y
x
3 is perpendicular to the line y
5
x.
6. The line y
2x
3 is parallel to the line y
4x
3.
7. The line 2y
3x
8 has a slope of 3.
8. Every straight line in the coordinate plane has an equation in standard
form.
9. The line x
2 is perpendicular to the line y
5.
10. The line y
x has no y-intercept.
4 . 3
E X E R C I S E S
3. What is the standard form for the equation of a line?
Reading and Writing After reading this section, write out
the answers to these questions. Use complete sentences.
1. What is the slope-intercept form for the equation of a
4. How can you graph a line when the equation is in slope-
line?
intercept form?
2. How can you determine the slope and y-intercept from
the slope-intercept form.
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