Question 1

Which of the following best describes the 'origin' on a Cartesian coordinate plane?

Accepted Answer

The point where the x-axis and y-axis intersect, at $$(0,0).$$

Question 2

Given the equation $$3x + 5y = 15$$, is the ordered pair $$(-5, 6) a $$solution?

Accepted Answer

Yes, because $$3(-5) + 5(6) = -15 + 30 = 15.$$

Question 3

Refer to the graph with points A, B, C, D, and E. Which point is located in Quadrant IV and what is its ordered pair?

Accepted Answer

Point C, $$(2, -5)$$

Question 4

Find the x-intercept and y-intercept of the equation $$6x - 2y = 12.$$

Accepted Answer

Question 5

What is the slope of the line passing through the points $$(-2, -5)$$ and $$(3, 10)$$?

Accepted Answer

$$m = \frac{10 - (-5)}{3 - (-2)} = \frac{15}{5} = 3$$

Question 6

Given the equation $$-5x + y = 7$$, solve for $$y$$ and identify the slope and y-intercept.

Accepted Answer

$$y = 5x + 7$$, slope = 5, y$$-$$intercept = 7

Question 7

Write the equation of the line passing through $$(-6, 1)$$ and $$(2, -5) in $$slope-intercept form.

Accepted Answer

$$y = -\frac{3}{4}x - 3.5$$

Question 8

Which of the following lines is perpendicular to the line $$y = 4x + 1$$?

Accepted Answer

$$y = -\frac{1}{4}x + 2$$

Question 9

Given the system $$\begin{cases} 6x - 2y = -2 \ 3x + y = -11 \end{cases}$$, is $$(-2, -5) a $$solution?

Accepted Answer

Yes, because both equations are satisfied when $$x = -2$$ and $$y = -5.$$

Question 10

Solve the system $$\begin{cases} x + y = 6 \ x - y = 2 \end{cases} by $$graphing or algebraically. What is the solution?

Accepted Answer

$$(4, 2)$$

Question 11

Solve the system $$\begin{cases} 3x + 2y = 14 \ 3x - 2y = 10 \end{cases}$$ using the addition method.

Accepted Answer

$$(4, 1)$$

Question 12

Which of the following best describes parallel lines?

Accepted Answer

Lines with the same slope but different y-intercepts.

Question 13

What is the equation of a line in standard form passing through $$(-3, 2)$$ and parallel to $$y = 4x + 1$$?

Accepted Answer

$$4x - y = -14$$

Question 14

Given the equation $$y = \frac{3}{4}x - 2$$, what are the slope and y-intercept?

Accepted Answer

Slope: $$\frac{3}{4}$$, y-intercept: $$-2$$

Question 15

Which of the following is the correct point-slope form for a line passing through $$(-2, 6)$$ with slope $$m = 5$$?

Accepted Answer

$$y - 6 = 5(x + 2)$$

Question 16

If a line has an undefined slope, which of the following best describes its orientation?

Accepted Answer

Vertical

Question 17

Solve the system $$\begin{cases} 6x + 8y = 15 \ 9x + 12y = 15 \end{cases}$$ using the addition method. What is the solution set?

Accepted Answer

No solution

Question 18

Which of the following is the correct standard form for the line with slope $$m = 5$$ passing through $$(−2, 6)$$?

Accepted Answer

$$5x - y = -16$$

Question 19

Which of the following best describes the y-intercept of a line?

Accepted Answer

The point where the line crosses the y-axis.

College Algebra Exam 3 Review – Graphs, Lines, and Systems

Study Guide - Practice Questions