4.3E: Exercises
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Identify the x- and y- Intercepts on a Graph
In the following exercises, find the x- and y- intercepts on each graph.
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(3,0),(0,3)
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(5,0),(0,−5)
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(−2,0),(0,−2)
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(−1,0),(0,1)
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(6,0),(0,3)
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(0,0)
Find the x- and y- Intercepts from an Equation of a Line
In the following exercises, find the intercepts for each equation.
x+y=4
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(4,0),(0,4)
x+y=3
x+y=−2
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(−2,0),(0,−2)
x+y=−5
x–y=5
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(5,0),(0,−5)
x–y=1
x–y=−3
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(−3,0),(0,3)
x–y=−4
x+2y=8
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(8,0),(0,4)
x+2y=10
3x+y=6
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(2,0),(0,6)
3x+y=9
x–3y=12
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(12,0),(0,−4)
x–2y=8
4x–y=8
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(2,0),(0,−8)
5x–y=5
2x+5y=10
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(5,0),(0,2)
2x+3y=6
3x–2y=12
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(4,0),(0,−6)
3x–5y=30
\(y=\frac{1}{3} x+1\)
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(-3,0),(0,1)
\(y=\frac{1}{4} x-1\)
\(y=\frac{1}{5} x+2\)
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(−10,0),(0,2)
\(y=\frac{1}{3} x+4\)
y=3x
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(0,0)
y=-2x
y=-4x
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(0,0)
y=5x
Graph a Line Using the Intercepts
In the following exercises, graph using the intercepts.
\(-x+5 y=10\)
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\(-x+4 y=8\)
\(x+2 y=4\)
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\(x+2 y=6\)
\(x+y=2\)
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\(x+y=5\)
\(x+y=-3\)
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\(x+y=-1\)
\(x-y=1\)
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\(x-y=2\)
\(x-y=-4\)
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\(x-y=-3\)
\(4 x+y=4\)
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\(3 x+y=3\)
\(2 x+4 y=12\)
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\(3 x+2 y=12\)
\(3 x-2 y=6\)
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\(5 x-2 y=10\)
\(2 x-5 y=-20\)
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\(3 x-4 y=-12\)
\(3 x-y=-6\)
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\(2 x-y=-8\)
\(y=-2 x\)
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\(y=-4 x\)
\(y=x\)
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y=3x
Everyday Math
Road trip. Damien is driving from Chicago to Denver, a distance of 1000 miles. The x- axis on the graph below shows the time in hours since Damien left Chicago. The y- axis represents the distance he has left to drive.
- Find the x- and y- intercepts.
- Explain what the x- and y- intercepts mean for Damien.
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- (0,1000),(15,0)
- At (0,1000), he has been gone 0 hours and has 1000 miles left. At (15,0), he has been gone 15 hours and has 0 miles left to go.
Road trip. Ozzie filled up the gas tank of his truck and headed out on a road trip. The x- axis on the graph below shows the number of miles Ozzie drove since filling up. The y- axis represents the number of gallons of gas in the truck’s gas tank.
- Find the x- and y- intercepts.
- Explain what the x- and y- intercepts mean for Ozzie.
Writing Exercises
How do you find the \(x\) -intercept of the graph of \(3 x-2 y=6 ?\)
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Answers will vary.
Do you prefer to use the method of plotting points or the method using the intercepts to graph the equation 4x+y=−4? Why?
Do you prefer to use the method of plotting points or the method using the intercepts to graph the equation \(y=\frac{2}{3}x−2\)? Why?
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Answers will vary.
Do you prefer to use the method of plotting points or the method using the intercepts to graph the equation y=6? Why?
Self Check
ⓐ After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section.
ⓑ What does this checklist tell you about your mastery of this section? What steps will you take to improve?