Question 1

Given the points $$(-4, -1)$$ and $$(4, 11)$$, what is the slope $$m of $$the line passing through them?

Accepted Answer

$$m = \frac{11 - (-1)}{4 - (-4)} = \frac{12}{8} = \frac{3}{2}$$

Question 2

What is the point-slope form of the equation of the line passing through $$(-4, -1)$$ and $$(4, 11)$$?

Accepted Answer

$$y + 1 = \frac{3}{2}(x + 4)$$

Question 3

Convert the point-slope form $$y + 1 = \frac{3}{2}(x + 4) to $$slope-intercept form.

Accepted Answer

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

Question 4

Which of the following is the correct slope-intercept form for the line passing through $$(-4, -1)$$ and $$(4, 11)$$?

Accepted Answer

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

Question 5

A line passes through $$(-4, -1)$$ and $$(4, 11). $$What is the $$y-$$intercept of this line?

Accepted Answer

$$5$$

Question 6

If a line passes through $$(-4, -1)$$ and $$(4, 11)$$, what is the equation of the line in point-slope form using the point $$(4, 11)$$?

Accepted Answer

$$y - 11 = \frac{3}{2}(x - 4)$$

Question 7

Which of the following points also lies on the line passing through $$(-4, -1)$$ and $$(4, 11)$$?

Accepted Answer

$$(0, 5)$$

Question 8

A chemical reaction produces a linear increase in temperature over time. If the temperature is $$-1^\circC at$$ $$t = -4$$ minutes and $$11^\circC at$$ $$t = 4$$ minutes, what is the equation relating temperature $$T to $$time $$t$$?

Accepted Answer

$$T = \frac{3}{2}t + 5$$

Question 9

If the equation of a line is $$y = \frac{3}{2}x + 5$$, what is the value of $$x$$ when $$y = 17$$?

Accepted Answer

$$8$$

Question 10

A medical researcher tracks the growth of bacteria in a petri dish. The population is $$-1 at$$ $$t = -4$$ hours and $$11 at$$ $$t = 4$$ hours. Assuming linear growth, what is the population at $$t = 0$$?

Accepted Answer

$$5$$

Question 11

Which of the following is NOT a valid way to write the equation of the line passing through $$(-4, -1)$$ and $$(4, 11)$$?

Accepted Answer

$$y - 4 = \frac{3}{2}(x - 11)$$

Question 12

If a line has equation $$y = \frac{3}{2}x + 5$$, what is the change in $$y as$$ $$x$$ increases from $$-4 to$$ $$4$$?

Accepted Answer

$$12$$

Question 13

Which of the following statements about the line passing through $$(-4, -1)$$ and $$(4, 11) is $$true?

Accepted Answer

The slope is positive and the line rises from left to right.

Question 14

If the equation of a line is $$y = \frac{3}{2}x + 5$$, what is the $$x-$$intercept?

Accepted Answer

$$x = -\frac{10}{3}$$

Question 15

A line passes through $$(-4, -1)$$ and $$(4, 11). If$$ $$y$$ represents profit in dollars and $$x$$ represents time in months, what is the average rate of change of profit per month?

Accepted Answer

$$\frac{3}{2}$$ dollars/month

Equations of a Line: Point-Slope and Slope-Intercept Forms

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