Question 1

Given the points $$(-3, -3)$$ and $$(6, 3)$$, what is the slope $$m of $$the line passing through these points?

Accepted Answer

$$m = \dfrac{3 - (-3)}{6 - (-3)} = \dfrac{6}{9} = \dfrac{2}{3}$$

Question 2

What is the equation of the line in slope-intercept form ($$y = mx + b) $$that passes through $$(-3, -3)$$ and $$(6, 3)$$?

Accepted Answer

$$y = \dfrac{2}{3}x - 1$$

Question 3

Which of the following is the equation of the line in point-slope form passing through $$(-3, -3)$$ with slope $$\dfrac{2}{3}$$?

Accepted Answer

$$y + 3 = \dfrac{2}{3}(x + 3)$$

Question 4

A line has a slope of $$\dfrac{1}{3}$$ and a $$y-$$intercept of $$-5. $$What is its equation in slope-intercept form?

Accepted Answer

$$y = \dfrac{1}{3}x - 5$$

Question 5

For the line $$y = \dfrac{1}{3}x - 5$$, what is the $$x-$$intercept?

Accepted Answer

$$x = 15$$

Question 6

Which of the following best describes the graph of the line $$y = \dfrac{2}{3}x - 1$$?

Accepted Answer

It rises from left to right and crosses the $$y-$$axis at $$-1.$$

Question 7

If a line passes through $$(6, 3)$$ and has a slope of $$\dfrac{2}{3}$$, what is its equation in point-slope form?

Accepted Answer

$$y - 3 = \dfrac{2}{3}(x - 6)$$

Question 8

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

Accepted Answer

$$T = 3t + 20$$

Question 9

A patient’s blood sugar level $$B (in mg/dL) $$decreases linearly after taking insulin. If $$B = 180 at$$ $$t = 0$$ minutes and $$B = 120 at$$ $$t = 30$$ minutes, what is the rate of change of $$B$$ with respect to $$t$$?

Accepted Answer

$$-2 mg/dL $$per minute

Question 10

A taxi charges a flat fee of $$\4$ plus $$\$$2$$ per mile. Which equation models the total cost $$C$$ for $$m$$ miles?

Accepted Answer

$$C = 2m + 4$$

Question 11

A line passes through $$(0, -5)$$ and has a slope of $$\dfrac{1}{3}. $$What is the $$y-$$coordinate when $$x = 6$$?

Accepted Answer

$$-3$$

Question 12

Which of the following points lies on the line $$y = \dfrac{2}{3}x - 1$$?

Accepted Answer

$$(3, 1)$$

Question 13

If the $$x-$$intercept of a line is $$x = 15$$ and the $$y-$$intercept is $$-5$$, what is the slope of the line?

Accepted Answer

$$\dfrac{1}{3}$$

Question 14

A line has the equation $$y = mx + b. If$$ $$m \u003e 0$$ and $$b \u003c 0$$, which quadrant does the line cross the $$y-$$axis?

Accepted Answer

Quadrant IV

Question 15

A business’s profit $$P (in $$dollars) is modeled by $$P = 50x - 200$$, where $$x is $$the number of units sold. What is the break-even point (where $$P = 0$$)?

Accepted Answer

$$x = 4$$

Equations of Lines and Their Graphs

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