Question 1

Given the equation of a line in slope-intercept form $$y = mx + b$$, what is the slope of the line passing through the points $$(2, 3)$$ and $$(5, 11)$$?

Accepted Answer

$$m = \frac{11 - 3}{5 - 2} = \frac{8}{3}$$

Question 2

Which of the following equations represents a line with a slope of $$-2$$ and a $$y-$$intercept of $$5$$?

Accepted Answer

$$y = -2x + 5$$

Question 3

A chemical reaction's rate is modeled by the linear equation $$y = 3x + 2$$, where $$x is $$time in seconds and $$y is $$concentration. What is the concentration after $$4$$ seconds?

Accepted Answer

$$y = 3(4) + 2 = 14$$

Question 4

Which of the following graphs represents the equation $$x = 2$$?

Accepted Answer

A vertical line passing through $$x = 2$$

Question 5

If a line passes through the points $$(0, 0)$$ and $$(4, 8)$$, what is its equation in slope-intercept form?

Accepted Answer

$$y = 2x$$

Question 6

A medical dosage increases linearly over time according to $$y = 0.5x + 1$$, where $$x is $$hours and $$y is $$dosage in mg. What is the dosage after $$6$$ hours?

Accepted Answer

$$y = 0.5(6) + 1 = 4$$

Question 7

Which of the following is the equation of a line parallel to $$y = -3x + 7$$ and passing through the point $$(1, 2)$$?

Accepted Answer

$$y = -3x + 5$$

Question 8

A business's profit is modeled by $$y = 4x - 10$$, where $$x is $$the number of products sold. How many products must be sold for the profit to be zero?

Accepted Answer

$$x = \frac{10}{4} = 2.5$$

Question 9

Which of the following is the equation of a line perpendicular to $$y = \frac{1}{2}x - 3$$ and passing through $$(0, 4)$$?

Accepted Answer

$$y = -2x + 4$$

Question 10

A line passes through $$(3, 7)$$ and has a slope of $$-4. $$What is its equation in point-slope form?

Accepted Answer

$$y - 7 = -4(x - 3)$$

Question 11

Which of the following lines has a $$y-$$intercept of $$-2$$?

Accepted Answer

$$y = 5x - 2$$

Question 12

A line passes through $$(0, 5)$$ and $$(2, 1). $$What is its equation in slope-intercept form?

Accepted Answer

$$y = -2x + 5$$

Question 13

Which of the following equations represents a horizontal line?

Accepted Answer

$$y = 4$$

Question 14

A line has the equation $$y = 7x - 3. $$What is the $$y-$$coordinate when $$x = -2$$?

Accepted Answer

$$y = 7(-2) - 3 = -14 - 3 = -17$$

Question 15

Which of the following is the equation of a line with slope $$0$$ passing through $$(5, -3)$$?

Accepted Answer

$$y = -3$$

Study Notes: Graphs of Linear Equations and the Equation $x = 2$

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