Question 1

Which of the following is the correct slope-intercept form of the equation of a line with slope $$m = -\frac{5}{4}$$ and $$y-$$intercept $$b = -2$$?

Accepted Answer

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

Question 2

Given the equation $$3y + 2x = 9$$, what is the slope of the line?

Accepted Answer

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

Question 3

A line passes through the point $$(-2, 5)$$ and has a slope of $$\frac{1}{3}. $$Which of the following is its equation in slope-intercept form?

Accepted Answer

$$y = \frac{1}{3}x + \frac{11}{3}$$

Question 4

Which of the following equations represents a vertical line passing through the point $$(4, -3)$$?

Accepted Answer

$$x = 4$$

Question 5

What is the equation of the line passing through the points $$(-4, 3)$$ and $$(5, 7) in $$standard form?

Accepted Answer

$$4x - 9y = -11$$

Question 6

If a line has a slope of $$0$$ and passes through the point $$(2, 6)$$, what is its equation?

Accepted Answer

$$y = 6$$

Question 7

Which of the following statements is true about the slope of a vertical line?

Accepted Answer

The slope is undefined.

Question 8

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

Accepted Answer

$$y + 2 = -4(x - 3)$$

Question 9

A line passes through $$(0, 6)$$ and $$(3, 0). $$What is its slope?

Accepted Answer

$$-2$$

Question 10

Which of the following is the equation of a line parallel to $$y = 2x + 5$$ and passing through $$(1, -3)$$?

Accepted Answer

Question 11

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

Accepted Answer

$$y = 2x + 3$$

Question 12

A real-world scenario: A taxi company charges a flat fee of $$\3$ plus $$\$$2$$ per mile. Which equation models the total cost $$C$$ for $$m$$ miles?

Accepted Answer

$$C = 2m + 3$$

Question 13

Given the equation $$y = mx + b$$, what does the $$b$$ represent in the context of a real-world problem?

Accepted Answer

The $$y-$$intercept, or the starting value when $$x = 0$$

Question 14

If a horizontal line passes through the point $$(7, -2)$$, what is its equation?

Accepted Answer

$$y = -2$$

Question 15

Which of the following is the correct point-slope form for a line with slope $$m$$ passing through $$(x_1$, y_1$)$$?

Accepted Answer

$$y - y_1$ = m(x - x_1$)$$

Question 16

A line passes through $$(2, 5)$$ and $$(6, 13). $$What is its equation in slope-intercept form?

Accepted Answer

$$y = 2x + 1$$

Question 17

Which of the following best describes the graph of $$y = 4$$?

Accepted Answer

A horizontal line passing through $$y = 4$$

Question 18

If a line has the equation $$x = -3$$, what can you say about its slope and direction?

Accepted Answer

The slope is undefined and the line is vertical.

Question 19

A biologist tracks the height $$h (in cm) of a $$plant over time $$t (in $$weeks) and finds the relationship $$h = 2t + 5. $$What does the $$2$$ represent in this context?

Accepted Answer

The plant grows $$2 cm $$per week.

Linear Equations, Graphs, and Functions: Writing Equations of Lines 2.3

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