Question 1

Use function notation to write the equation of the line with the given slope and y-intercept.&#10;

Accepted Answer

The equation of a line in slope-intercept form is $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept. Given a slope of $\frac{2}{5}$ and a y-intercept of $-8$, the equation becomes $f(x) = \frac{2}{5}x - 8$.

Question 2

Find an equation of the line with the given slope and containing the given point. Write the equation using function&#10;notation.&#10;

Accepted Answer

The equation of a line with slope $m$ and passing through the point $(x_1, y_1)$ is given by $y - y_1 = m(x - x_1)$. Substituting $m = \frac{4}{3}$ and the point $(0, 2)$ into this formula gives $y - 2 = \frac{4}{3}(x - 0)$, which simplifies to $y = \frac{4}{3}x + 2$, or in function notation, $f(x) = \frac{4}{3}x + 2$.

Question 3

Find an equation of the line with the given slope and containing the given point. Write the equation using function&#10;notation.&#10;

Accepted Answer

To find the equation of the line with slope $m = -\frac{2}{3}$ and passing through the point $(3,3)$, we use the point-slope form $y - y_1 = m(x - x_1)$, where $(x_1, y_1)$ is the given point. Substituting $m = -\frac{2}{3}$, $x_1 = 3$, and $y_1 = 3$, we get $y - 3 = -\frac{2}{3}(x - 3)$. Simplifying, we find $y = -\frac{2}{3}x + 3 + 2 = -\frac{2}{3}x + 5$, which corresponds to $f(x) = -\frac{2}{3}x + 5$.

Question 4

Find an equation of the line with the given slope and containing the given point. Write the equation using function&#10;notation.&#10;

Accepted Answer

The answer of Find an equation of the line with...

Question 5

Use function notation to write the equation of the line with the given slope and y-intercept.&#10;

Accepted Answer

The equation of a line in slope-intercept form is $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept. Given a slope of $\frac{4}{3}$ and a y-intercept of $-1$, the equation becomes $f(x) = \frac{4}{3}x - 1$.

Question 6

Use function notation to write the equation of the line with the given slope and y-intercept.&#10;

Accepted Answer

The equation of a line with slope $m$ and y-intercept $b$ is given by $y = mx + b$. Here, $m = -\frac{2}{3}$ and $b = 0$, so the equation becomes $f(x) = -\frac{2}{3}x$.

Question 7

Graph the linear function.&#10;

Accepted Answer

The answer of Graph the linear function.&#10; ...

Question 8

Match the linear function with its graph.&#10;

Accepted Answer

The answer of Match the linear function with its graph.&#10;...

Question 9

Find an equation of the line. Write the equation using function notation.&#10;

Accepted Answer

The slope of the line is $\frac { - 44 - ( - 4 ) } { - 9 - 1 } = \frac { - 40 } { - 10 } = 4$. The y-intercept is -8. So, the equation of the line is $y = 4 x - 8$. In function notation, this is $f ( x ) = 4 x - 8$.

Question 10

Match the linear function with its graph.&#10;

Accepted Answer

The answer of Match the linear function with its graph.&#10;...

Question 11

Graph the linear function.&#10;

Accepted Answer

The answer of Graph the linear function.&#10; ...

Question 12

Match the linear function with its graph.&#10;

Accepted Answer

The answer of Match the linear function with its graph.&#10;...

Question 13

Find an equation of the line with the given slope and containing the given point. Write the equation using function&#10;notation.&#10;

Accepted Answer

The answer of Find an equation of the line with...

Question 14

Match the linear function with its graph.&#10;

Accepted Answer

The answer of Match the linear function with its graph.&#10;...

Question 15

Find an equation of the line. Write the equation using function notation.&#10;

Accepted Answer

The answer of Find an equation of the line. Write...

Question 16

Graph the linear function.&#10;

Accepted Answer

The answer of Graph the linear function.&#10;   ...

Question 17

Find an equation of the line. Write the equation using function notation.&#10;

Accepted Answer

The answer of Find an equation of the line. Write...

Question 18

Graph the linear function.&#10;

Accepted Answer

The answer of Graph the linear function.&#10;   ...

Question 19

Graph the linear function.&#10;

Accepted Answer

The answer of Graph the linear function.&#10; ...

Question 20

Use function notation to write the equation of the line with the given slope and y-intercept.&#10;

Accepted Answer

The answer of Use function notation to write the equation...

Question 21

Find the equation of the line. Write the equation using standard notation.&#10;

Accepted Answer

The answer of Find the equation of the line. Write...

Question 22

Find an equation of the line. Write the equation using function notation.&#10;

Accepted Answer

The answer of Find an equation of the line. Write...

Question 23

Find an equation of the line. Write the equation using function notation.&#10;

Accepted Answer

The answer of Find an equation of the line. Write...

Question 24

Find the equation of the line. Write the equation using standard notation.&#10;

Accepted Answer

The answer of Find the equation of the line. Write...

Question 25

Find the equation of the line. Write the equation using standard notation.&#10;

Accepted Answer

The answer of Find the equation of the line. Write...

Question 26

Write an equation of the line using function notation.&#10;

Accepted Answer

The answer of Write an equation of the line using...

Question 27

Find the equation of the line. Write the equation using standard notation.&#10;

Accepted Answer

The answer of Find the equation of the line. Write...

Question 28

Find the equation of the line. Write the equation using standard notation.&#10;

Accepted Answer

The answer of Find the equation of the line. Write...

Question 29

Find an equation of the line. Write the equation using function notation.&#10;

Accepted Answer

The answer of Find an equation of the line. Write...

Question 30

Write an equation of the line using function notation.&#10;

Accepted Answer

The answer of Write an equation of the line using...

Question 31

Find an equation of the line. Write the equation using function notation.&#10;

Accepted Answer

The answer of Find an equation of the line. Write...

Question 32

Write an equation of the line using function notation.&#10;

Accepted Answer

The answer of Write an equation of the line using...

Question 33

Find an equation of the line. Write the equation using function notation.&#10;

Accepted Answer

The answer of Find an equation of the line. Write...

Question 34

Find the equation of the line. Write the equation using standard notation.&#10;

Accepted Answer

The answer of Find the equation of the line. Write...

Question 35

Write an equation of the line using function notation.&#10;

Accepted Answer

The answer of Write an equation of the line using...

Question 36

Find an equation of the line. Write the equation using function notation.&#10;

Accepted Answer

The answer of Find an equation of the line. Write...

Question 37

Find the equation of the line. Write the equation using standard notation.&#10;

Accepted Answer

The answer of Find the equation of the line. Write...

Question 38

Find the equation of the line. Write the equation using standard notation.&#10;

Accepted Answer

The answer of Find the equation of the line. Write...

Question 39

Find an equation of the line. Write the equation using function notation.&#10;

Accepted Answer

The answer of Find an equation of the line. Write...

Question 40

Find an equation of the line. Write the equation using function notation.&#10;

Accepted Answer

The answer of Find an equation of the line. Write...

Question 41

Solve.&#10;

Accepted Answer

The answer of Solve.&#10; ...

Question 42

Solve.&#10;

Accepted Answer

The answer of Solve.&#10; ...

Question 43

Solve.&#10;

Accepted Answer

The answer of Solve.&#10; ...

Question 44

Find an equation of the line graphed. Write the equation using function notation.&#10;

Accepted Answer

The answer of Find an equation of the line graphed....

Question 45

Solve.&#10;

Accepted Answer

The answer of Solve.&#10; ...

Question 46

Find an equation of the line graphed. Write the equation using function notation.&#10;

Accepted Answer

The answer of Find an equation of the line graphed....

Question 47

Solve.&#10;The total sales made by a salesperson was $25,000 after 3 months and $68,000 after 23 months. Find an equation relating time and sales. Use the equation to predict the total sales after 42 months.&#10;A) $108,850&#10;B) $108,820&#10;C) $108,892&#10;D) $108,950

Accepted Answer

The answer of Solve.&#10;The total sales made by a salesperson...

Question 48

Find an equation of the line graphed. Write the equation using function notation.&#10;

Accepted Answer

The answer of Find an equation of the line graphed....

Question 49

Find the equation of the line. Write the equation using standard notation.&#10;

Accepted Answer

The answer of Find the equation of the line. Write...

Question 50

Solve.&#10;

Accepted Answer

The answer of Solve.&#10; ...

Question 51

Solve.&#10;In 2010 a certain county recovered 27% of its municipal wastes through recycling, up from 17% in 2005. Find a linear equation that fits this data. Use this equation to predict the percentage recycled&#10;In 2021.&#10;A) 45.4%&#10;B) 47.1%&#10;C) 50.7%&#10;D) 49%

Accepted Answer

The answer of Solve.&#10;In 2010 a certain county recovered 27%...

Question 52

Solve.&#10;In 2005, John invested $19,000 in the stock market. By 2010 his investment had grown to $23,700. Find an equation relating time and the value of the investment. If the market continues to grow at&#10;The same rate, how much will be in his account in 2017? Round to the nearest dollar.&#10;A) $28,400&#10;B) $30,280&#10;C) $25,581&#10;D) $23,701

Accepted Answer

The answer of Solve.&#10;In 2005, John invested $19,000 in the...

Question 53

Find the equation of the line. Write the equation using standard notation.&#10;

Accepted Answer

The answer of Find the equation of the line. Write...

Question 54

Find the equation of the line. Write the equation using standard notation.&#10;

Accepted Answer

The answer of Find the equation of the line. Write...

Question 55

Find the equation of the line. Write the equation using standard notation.&#10;

Accepted Answer

The answer of Find the equation of the line. Write...

Question 56

Solve.&#10;

Accepted Answer

The answer of Solve.&#10; ...

Question 57

Find the equation of the line. Write the equation using standard notation.&#10;

Accepted Answer

The answer of Find the equation of the line. Write...

Question 58

Solve.&#10;

Accepted Answer

The answer of Solve.&#10; ...

Question 59

Solve.&#10;

Accepted Answer

The answer of Solve.&#10; ...

Question 60

Solve.&#10;

Accepted Answer

The answer of Solve.&#10; ...

Question 61

Use the given graph of the function.&#10;

Accepted Answer

The answer of Use the given graph of the function.&#10;...

Question 62

Solve.&#10;The amount of water in a leaky bucket is given by the linear function f(t) = 125 - 9t, where f(t) is in ounces and t is in minutes. Find the amount of water in the bucket after 9 minutes.&#10;A) 81 ounces&#10;B) 44 ounces&#10;C) 206 ounces&#10;D) 116 ounces

Accepted Answer

The answer of Solve.&#10;The amount of water in a leaky...

Question 63

Find the square root.&#10;

Accepted Answer

The answer of Find the square root.&#10; ...

Question 64

Find the square root.&#10;

Accepted Answer

The answer of Find the square root.&#10; ...

Deck 8: More on Functions and Graphs