Download Determine whether each equation is a linear equation. Write yes or

Mid-Chapter Quiz
Determine whether each equation is a linear equation. Write yes or no. If yes, write the equation in
standard form.
y = 4x + 3
Rewrite the equation in standard form.
The equation is now in standard form where A = 4, B = 1, and C = 3. The equation is linear.
2
x + 3y = 8
Because x is squared, the equation cannot be written in standard form. The equation is not linear.
Rewrite the equation in standard form.
The equation is now in standard form where A = 1, B = 3, and C = 4. The equation is linear.
Graph each equation using the x and y intercepts.
y = 3x 6
To graph the equation, find the x- and y-intercepts. Plot these two points. Then draw a line through them.
To find the x-intercept, let y = 0.
To find the y-intercept, let x = 0.
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Page 1
Mid-Chapter Quiz
The equation is now in standard form where A = 1, B = 3, and C = 4. The equation is linear.
Graph each equation using the x and y intercepts.
y = 3x 6
To graph the equation, find the x- and y-intercepts. Plot these two points. Then draw a line through them.
To find the x-intercept, let y = 0.
To find the y-intercept, let x = 0.
So, the x-intercept is 2 and the y-intercept is 6.
2x + 5y = 10
To graph the equation, find the x- and y-intercepts. Plot these two points. Then draw a line through them.
To find the x-intercept, let y = 0.
To find the y-intercept, let x = 0.
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Mid-Chapter Quiz
2x + 5y = 10
To graph the equation, find the x- and y-intercepts. Plot these two points. Then draw a line through them.
To find the x-intercept, let y = 0.
To find the y-intercept, let x = 0.
So, the x-intercept is 5 and the y-intercept is 2.
Graph each equation by making a table.
y = 2x
To make the table of values, start at x = 0 and evaluate y. Continue this process for other values of x. Plot the points
and draw a line through them.
x
2
1
0
1
2
y
4
2
0
2
4
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points
( 2, 4)
( 1, 2)
(0, 0)
(1, 2)
(2, 4)
Page 3
Mid-Chapter Quiz
Graph each equation by making a table.
y = 2x
To make the table of values, start at x = 0 and evaluate y. Continue this process for other values of x. Plot the points
and draw a line through them.
x
2
1
0
1
2
y
4
2
0
2
4
points
( 2, 4)
( 1, 2)
(0, 0)
(1, 2)
(2, 4)
x=8 y
To make the table of values, start at x = 0 and evaluate y. Continue this process for other values of x. Plot the points
and draw a line through them.
x
y
points
2
10
( 2, 10)
1
9
( 1, 9)
0
8
(0, 8)
1
7
(1, 7)
2
6
(2, 6)
BOOK SALES The equation 5x + 12y = 240 describes the total amount of money collected when selling x
paperback books at $5 per book and y hardback books at $12 per book. Graph the equation using the x- and yintercepts.
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To graph
equation,
find the
x- and y-intercepts. Plot these two points. Then draw a line through them.
To find the x-intercept, let y = 0.
Page 4
Mid-Chapter Quiz
BOOK SALES The equation 5x + 12y = 240 describes the total amount of money collected when selling x
paperback books at $5 per book and y hardback books at $12 per book. Graph the equation using the x- and yintercepts.
To graph the equation, find the x- and y-intercepts. Plot these two points. Then draw a line through them.
To find the x-intercept, let y = 0.
To find the y-intercept, let x = 0.
So, the x-intercept is 48 and the y-intercept is 20.
Find the root of each equation.
x+8=0
The root, or solution, of an equation is any value that makes the equation true.
So, the root is 8.
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4x
24 = 0
Page 5
Mid-Chapter Quiz
Find the root of each equation.
x+8=0
The root, or solution, of an equation is any value that makes the equation true.
So, the root is 8.
4x
24 = 0
The root, or solution, of an equation is any value that makes the equation true.
So, the root is 6.
18 + 8x = 0
The root, or solution, of an equation is any value that makes the equation true.
So, the root is
.
The root, or solution, of an equation is any value that makes the equation true.
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Mid-Chapter
So, the rootQuiz
is
.
The root, or solution, of an equation is any value that makes the equation true.
So, the root is .
Solve each equation by graphing.
5x + 35 = 0
The related function is y = 5x + 35.
The graph intersects the x-axis at 7. So, the solution is 7.
14x
84 = 0
The related function is y = 14x
84.
The graph intersects the x-axis at 6. So, the solution is 6.
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118 + 11x = 3
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Mid-Chapter
The graphQuiz
intersects the x-axis at 7. So, the solution is 7.
14x
84 = 0
The related function is y = 14x
84.
The graph intersects the x-axis at 6. So, the solution is 6.
118 + 11x = 3
The related function is y = 11x + 121.
The graph intersects the x-axis at 11. So, the solution is 11.
MULTIPLE CHOICE
The function y = 15 + 3x represents the outside temperature, in degrees Fahrenheit, in a small Alaskan town where
x represents the number of hours after midnight. The function is accurate for x values representing midnight through
4:00 p.m. Find the zero of this function.
0
3
5
15
The zero is located at the x-intercept of the function. To find the x-intercept, let y = 0.
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The zero is 5. The correct choice is C.
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Mid-Chapter Quiz
The graph intersects the x-axis at 11. So, the solution is 11.
MULTIPLE CHOICE
The function y = 15 + 3x represents the outside temperature, in degrees Fahrenheit, in a small Alaskan town where
x represents the number of hours after midnight. The function is accurate for x values representing midnight through
4:00 p.m. Find the zero of this function.
0
3
5
15
The zero is located at the x-intercept of the function. To find the x-intercept, let y = 0.
The zero is 5. The correct choice is C.
Find the rate of change represented in the table.
To find the rate of change, use the coordinates (1, 2) and (4, 6).
So, the rate of change is
.
Find the slope of the line that passes through each pair of points.
(2, 6), (4, 12)
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Mid-Chapter
So, the rateQuiz
of change is
.
Find the slope of the line that passes through each pair of points.
(2, 6), (4, 12)
So, the slope is 3.
(1, 5), (3, 8)
So, the slope is
.
( 3, 4), (2, 6)
So, the slope is 2.
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Mid-Chapter Quiz
So, the slope is 2.
So, the slope is
.
MULTIPLE CHOICE
Find the value of r so the line that passes through the pair of points has the given slope.
( 4, 8), (r, 12), m =
4
1
0
3
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The correct choice is G.
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Mid-Chapter
Quiz
So, the slope
is
.
MULTIPLE CHOICE
Find the value of r so the line that passes through the pair of points has the given slope.
( 4, 8), (r, 12), m =
4
1
0
3
The correct choice is G.
Find the slope of the line that passes through the pair of points.
So, the slope is 12.
POPULATION GROWTH
The graph shows the population growth in Heckertsville since 2003.
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Mid-Chapter Quiz
So, the slope is 12.
POPULATION GROWTH
The graph shows the population growth in Heckertsville since 2003.
a. For which time period is the rate of change the greatest?
b. Explain the meaning of the slope from 2003 to 2009.
a. Looking at the graph, the slope is the steepest from 2006 2007, so the rate of change for that period is the
greatest.
b. The population changed from about 16,000 to about 19,700 from 2003 to 2009. Find the slope.
So, the average rate of change in population is about 630. This means that there was an average increase of about
630 people per year in Heckertsville between 2003 and 2009.
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