Question 1

Which of the following is the correct slope-intercept form of the line passing through the points $$(2, 7)$$ and $$(6, 3)$$?

Accepted Answer

$$y = -1x + 9$$

Question 2

A line passes through the point $$(5, -2)$$ and has a slope of $$\frac{3}{4}. $$What is its equation in point-slope form?

Accepted Answer

$$y = \frac{3}{4}(x - 5) - 2$$

Question 3

Which of the following lines is parallel to $$y = -\frac{2}{5}x + 7$$ and passes through $$(0, -3)$$?

Accepted Answer

$$y = -\frac{2}{5}x - 3$$

Question 4

Find the equation, in slope-intercept form, of the line perpendicular to $$3x - 4y = 8$$ and passing through $$(4, 1).$$

Accepted Answer

$$y = -\frac{4}{3}x + \frac{19}{3}$$

Question 5

A chemical reaction's temperature $$T (in$$ $$^C) $$increases linearly with time $$t (in $$minutes). At $$t = 0$$, $$T = 20^C$$; at $$t = 10$$, $$T = 50^C. $$What is the linear equation relating $$T$$ and $$t$$?

Accepted Answer

$$T = 3t + 20$$

Question 6

Given the line $$y = 4x - 7$$, what is the equation of the line perpendicular to it and passing through the point $$(2, 5)$$? Express your answer in slope-intercept form.

Accepted Answer

$$y = -\frac{1}{4}x + 5.5$$

Question 7

A company’s profit $$P (in $$thousands of dollars) is modeled by a linear function of the number of units sold $$n. If$$ $$P = 10$$ when $$n = 100$$ and $$P = 22$$ when $$n = 250$$, what is the equation for $$P in $$terms of $$n$$?

Accepted Answer

$$P = 0.08n + 2$$

Question 8

Find the $$x-$$intercept and $$y-$$intercept of the line $$7x + 2y = 14.$$

Accepted Answer

$$x-$$intercept: $$(2, 0)$$; $$y-$$intercept: $$(0, 7)$$

Question 9

A hospital records the number of flu cases $$C as a $$linear function of the week $$w$$ since the start of the year. If $$C = 120 at$$ $$w = 4$$ and $$C = 180 at$$ $$w = 10$$, what is the predicted number of cases at $$w = 15$$?

Accepted Answer

$$C = 230$$

Question 10

Which of the following statements about the slopes of parallel and perpendicular lines is TRUE?

Accepted Answer

Parallel lines have equal slopes; perpendicular lines have slopes that are negative reciprocals of each other.

Question 11

A line passes through $$(1, 2)$$ and is perpendicular to the line $$y = -\frac{1}{3}x + 4. $$What is the equation of the line in slope-intercept form?

Accepted Answer

$$y = 3x - 1$$

Question 12

If a line has the equation $$2x - 5y = 10$$, what is its slope?

Accepted Answer

$$\frac{2}{5}$$

Question 13

A city’s population $$P (in $$thousands) grew linearly from $$P = 80 in 2000 to$$ $$P = 104 in 2010. $$Let $$t be $$the number of years since 2000. What is the linear function $$P(t)$$?

Accepted Answer

$$P(t) = 2.4t + 80$$

Question 14

Which of the following is the correct point-slope form for the line passing through $$(7, -3)$$ with slope $$-\frac{5}{2}$$?

Accepted Answer

$$y = -\frac{5}{2}(x - 7) - 3$$

Question 15

A biologist observes that the height $$h (in cm) of a $$plant increases linearly with time $$t (in $$weeks). If $$h = 12 at$$ $$t = 2$$ and $$h = 24 at$$ $$t = 8$$, what is the predicted height at $$t = 12$$?

Accepted Answer

$$h = 36$$

Question 16

Given the line $$y = -\frac{3}{2}x + 4$$, what is the slope of a line perpendicular to it?

Accepted Answer

$$\frac{2}{3}$$

Question 17

A line passes through $$(0, 8)$$ and is parallel to the line $$y = 7x - 2. $$What is its equation?

Accepted Answer

$$y = 7x + 8$$

Question 18

If the equation of a line is $$y = mx + b$$ and the line passes through $$(3, 7)$$ and $$(6, 13)$$, what is the value of $$m$$?

Accepted Answer

$$2$$

Question 19

A researcher finds that the concentration $$C (in mg/L) of a $$substance in a solution decreases linearly from $$C = 50 at$$ $$t = 0$$ hours to $$C = 35 at$$ $$t = 3$$ hours. What is the linear equation for $$C in $$terms of $$t$$?

Accepted Answer

$$C = -5t + 50$$

Equations of Lines: Forms, Properties, and Applications

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