Algebra - Lines & Slopes MCQs Practice

Answers will be provided at the end

Practice Drill - Lines and Slope

Practice Drill - Lines and Slope

(If timing, take about 12 minutes to complete.)
Question 1
Which of the following equations represents a line in the xy-coordinate plane with a y-intercept of 6 and a slope of -3?
Correct Answer: D
Use the slope-intercept form of a line, and plug in the value for the slope, m, and the y-intercept, b.
y = mx + b → y = -3x + 6
Question 2
In the xy-plane, which of these linear equations has a y-intercept of 12?
Correct Answer: A
When a line is written in slope-intercept form, the y-intercept corresponds to the constant b. The only option that has positive 12 for b is choice (A).
y = mx + b → y = 4x + 12
Question 3
A linear equation in the xy-plane intercepts the y-axis at -3. For every 2 units the y-coordinate of the line increases, the x-coordinate decreases by 7 units. Which of the following is the correct equation for this line?
Correct Answer: C
From the description of the line in the problem, we can determine the line's slope. The line decreases horizontally 7 units for every 2 units it increases vertically. Therefore, the slope of the line will be 2 / (-7) = -2/7.
The only option that has -2/7 for its slope is choice (C).
Question 4
Consider the graph of the line above as graphed in the xy-coordinate plane. What is the value of b if the line is presented in the equation y = mx + b in which both m and b are constants?
10 5 0 -5 -5 5 10 y x
Correct Answer: B
The line intersects the y-axis at the point (0,8). Therefore, the y-intercept of the line is 8.
Question 5
What is the slope of a line with the equation 5x + 4y = 2?
Correct Answer: C
Put the line in slope-intercept form in order to determine the slope of the line:
5x + 4y = 2 →
4y = -5x + 2 →
y = -(5/4)x + 2/4 → y = -(5/4)x + 1/2
So, the slope of the line is -5/4.
Question 6
For the equation (1/2)y = (2/3)x - 4, what is the x-intercept?
Correct Answer: D
This is an easy question to misread-you are asked to find the x-intercept, not the y-intercept. The x-intercept is the point at which the line intersects the x-axis; for this to happen, the y value at the point must be zero. So, plug zero in for y and see what the value of x is:
(1/2)y = (2/3)x - 4 →
(1/2)(0) = (2/3)x - 4 →
0 = (2/3)x - 4 → 4 = (2/3)x →
x = 4 × (3/2) → x = 12/2 = 6
Question 7
Two lines are graphed in the xy-plane. The lines have the same slope and different y-intercepts. How many solution(s) would the equations represented by this pair of lines have?
Correct Answer: A
Lines that have the same slope and different y-intercepts run parallel to one another. At no point will they intersect, so the answer is "none."
Question 8
Which of these represents a linear equation in the xy-plane that has the points (5, 17) and (2, 5)?
Correct Answer: C
Looking ahead to the answers, all of the choices have different values for the line's slope. So, calculate the slope of the line with the given information and see which of the options matches:
Slope = (y2 - y1) / (x2 - x1) = (17 - 5) / (5 - 2) = 12 / 3 = 4
The only one of the lines that has 4 as its slope is choice (C), y = 4x - 3.
Question 9
The above graph is represented by which of these sets of equations?
6 4 2 0 -2 2 4 6 8 -2 -4 y x
Correct Answer: B
Fortunately, the different options given have different y-intercepts. So you can save time in solving this by identifying the y-intercepts of the two lines and then matching them with a choice. The two y-intercepts are 5 and -4, and the only option that has both of those values as y-intercepts is choice (B):
y = 2x - 4
y = -x + 5
Question 10
Which of the following equations has a slope perpendicular to the slope of a line with the equation y = ax + b given that a and b are constants?
Correct Answer: A
Since the equation of the line is already in slope-intercept form, we can see that its slope is a. We then can take the negative reciprocal of a.