Question 1

What is the slope of the line passing through the points $$ (1, -5) $$ and $$ (-4, 3) $$?

Accepted Answer

$$ m = \frac{8}{5} $$

Question 2

Given the equation $$ y = -2x + 3 $$, what is the y-intercept of the line?

Accepted Answer

$$ (0, 3) $$

Question 3

Write the equation of the line in slope-intercept form that passes through the point $$ (3, 2) $$ with a slope of $$ -1 . $$

Accepted Answer

$$ y = -x + 5 $$

Question 4

Given the points $$ (-1, 4) $$ and $$ (2, -3) $$, what is the equation of the line in slope-intercept form?

Accepted Answer

$$ y = -\frac{7}{3}x + \frac{11}{3} $$

Question 5

The relationship between Fahrenheit temperature $$ F $$ and Celsius temperature $$ C  is $$linear. Using the points $$ (0, 32) $$ and $$ (100, 212) $$, what is the equation expressing $$ F  in $$terms of $$ C $$?

Accepted Answer

$$ F = 1.8C + 32 $$

Question 6

If the temperature is $$ 30^\circ C $$, what is the temperature in Fahrenheit using the formula $$ F = 1.8C + 32 $$?

Accepted Answer

$$ 86^\circ F $$

Question 7

Given the data points $$ (326, 57.06) $$ and $$ (385, 57.99) $$ for atmospheric CO$$_2$$ concentration $$ x $$ and average global temperature $$ f(x) $$, what is the slope of the linear function modeling this relationship? (Round to two decimal places)

Accepted Answer

$$ m = 0.016 $$

Question 8

Using your answer from the previous question, what is the linear function $$ f(x)  in $$slope-intercept form that models the average global temperature for atmospheric CO$$_2$$ concentration $$ x $$? (Round to two decimal places)

Accepted Answer

$$ f(x) = 0.016x + 51.82 $$

Question 9

According to the graph of living arrangements, what is the equation in slope-intercept form for the percentage $$ f(x)  of $$young adults who own a home, $$ x $$ years after 2000, using the points $$ (0, 45.4) $$ and $$ (17, 38.4) $$? (Round to the nearest tenth)

Accepted Answer

$$ f(x) = -0.4x + 45.4 $$

Question 10

For the percentage $$ g(x)  of $$young adults living with parents, $$ x $$ years after 2000, what is the equation in slope-intercept form using the points $$ (0, 11.9) $$ and $$ (17, 22.0) $$? (Round to the nearest tenth)

Accepted Answer

$$ g(x) = 0.6x + 11.9 $$

Question 11

If the trends continue, in what year will the percentage of young adults owning a home be the same as the percentage living with their parents? (Use $$ f(x) = -0.4x + 45.4 $$ and $$ g(x) = 0.6x + 11.9 )$$

Accepted Answer

$$ 2040 $$

Question 12

Using the points $$ (10, 24.6) $$ and $$ (20, 25.8) $$ from the one-person household data, what is the point-slope form of the equation modeling the percentage $$ y  of $$one-person households $$ x $$ years after 1980?

Accepted Answer

$$ y - 24.6 = 0.12(x - 10) $$

Question 13

Convert the previous answer to slope-intercept form and write it as a function $$ f(x) .$$

Accepted Answer

$$ f(x) = 0.12x + 23.4 $$

Question 14

If the trend continues, in what year will the percentage of one-person households reach 30%? (Use $$ f(x) = 0.12x + 23.4 )$$

Accepted Answer

$$ 2045 $$

Question 15

A city’s temperature in Fahrenheit is modeled by $$ F = 1.8C + 32 . If $$the temperature increases by $$ 10^\circ C $$, by how many degrees Fahrenheit does the temperature increase?

Accepted Answer

$$ 18^\circ F $$

Question 16

Suppose the average global temperature is $$ 57.5^\circ F . $$Using the model $$ f(x) = 0.016x + 51.82 $$, estimate the atmospheric CO$$_2$$ concentration $$ x  (in $$parts per million).

Accepted Answer

$$ 355.6 $$

Linear Functions and Slope: Applications and Modeling

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