1.
Which equation describes the line with a slope of 2 that contains the point (4, -3)?
Correct Answer
C. Y + 3 = 2(x - 4)
Explanation
The equation y + 3 = 2(x - 4) describes the line with a slope of 2 that contains the point (4, -3). This equation is in the form y = mx + b, where m represents the slope and b represents the y-intercept. In this equation, the slope is 2 and the point (4, -3) satisfies the equation when plugged in. Therefore, this equation accurately describes the line with the given conditions.
2.
Here are four linear equations:
I. 4x + 3y = 15
II. 3x - 4y = -8
III.
IV.
Which pair of lines are parallel?
Correct Answer
C. II and IV
Explanation
The pair of lines that are parallel are II and IV. This can be determined by comparing the slopes of the lines. The equation of a line can be written in the form y = mx + b, where m is the slope of the line. In equations II and IV, the coefficient of x is the same (-4), indicating that the slopes of these lines are equal. Therefore, II and IV are parallel lines.
3.
Which equation describes a line
that passes through (-6, 8) and is
perpendicular to the line described
by y= 2x - 4?
Correct Answer
B.
Explanation
The equation that describes a line passing through (-6, 8) and is perpendicular to the line y = 2x - 4 is y = -1/2x + 5. This is because the slope of the given line is 2, so the slope of the perpendicular line would be -1/2 (the negative reciprocal). The y-intercept of the perpendicular line can be found by substituting the coordinates of the given point (-6, 8) into the equation.
4.
Correct Answer
C. C
5.
A vacation home in Orlando, Florida, rents for $105 per day. The function f(x) = 105x gives the cost of renting the home for x days. What is the domain of this function?
Correct Answer
B. (0, 1, 2, 3,...)
Explanation
The domain of a function represents the set of all possible input values for the function. In this case, the function f(x) = 105x represents the cost of renting the home for x days. Since the number of days cannot be negative, the domain of this function would be all positive integers starting from 0. Therefore, the correct answer is (0, 1, 2, 3,...).
6.
A parking meter gives 30 minutes for
each quarter and 6 minutes for each
nickel. The equation 30x + 6y = 60
describes the number of quarters x
and nickels y that you need to park for
60 minutes. What does the x-intercept
represent?
Correct Answer
A. You need 2 quarters and no nickels to
park for 60 minutes.
Explanation
The x-intercept represents the number of quarters needed to park for 60 minutes without using any nickels. In this case, the x-intercept is 2, indicating that 2 quarters are required to park for the full duration.
7.
This table shows the U.S. federal minimum hourly wage in different years. During which time interval did the wage increase at the greatest rate?
Correct Answer
D. 1990 to 1991
Explanation
The wage increase at the greatest rate occurred during the time interval of 1990 to 1991.
8.
Find the slope of this line.
Correct Answer
D.
9.
Find the slope of the line that contains the points (1, -1) and (-2, 8)
Correct Answer
B. -3
Explanation
To find the slope of a line passing through two points, we can use the formula: slope = (change in y)/(change in x).
Using the points (1, -1) and (-2, 8), we can calculate the change in y as -1 - 8 = -9, and the change in x as 1 - (-2) = 3.
Therefore, the slope of the line is -9/3 = -3.
10.
Which equation is NOT a direct variation?
Correct Answer
B. 5x + 2y = 10
Explanation
The equation 5x + 2y = 10 is not a direct variation because it does not represent a relationship where one variable is directly proportional to the other. In a direct variation, the equation would be in the form y = kx, where k is a constant. However, in this equation, there is a constant term (10) and the variables (x and y) are not directly proportional to each other. Therefore, it does not represent a direct variation.
11.
Which equation describes the line with a slope of 5 and y-intercept of -3?
Correct Answer
C. Y = 5x - 3
Explanation
The equation y = 5x - 3 describes the line with a slope of 5 and y-intercept of -3. The slope of 5 indicates that for every increase of 1 in the x-coordinate, the y-coordinate increases by 5. The y-intercept of -3 means that the line crosses the y-axis at the point (0, -3). Therefore, the equation y = 5x - 3 represents a line with a slope of 5 and a y-intercept of -3.
12.
Which graph shows the use of slope-intercept form to graph the equation y= -1/4x + 3
Correct Answer
D. D
13.
Graph f(x) = -3x + 4 and g(x) = 3x + 4. Which describes the transformation(s) from the graph of f(x) to the graph of g(x)?
Correct Answer
A. A reflection across the y-axis
Explanation
The graph of g(x) is obtained by reflecting the graph of f(x) across the y-axis. This means that each point on the graph of f(x) is transformed to a point on the graph of g(x) with the same x-coordinate but opposite y-coordinate. Therefore, the correct answer is a reflection across the y-axis.
14.
What is the equation of the line that has a
slope of -2/3 and passes through the
point (6, 1)?
Correct Answer
B. Y = -2/3 + 5
Explanation
The equation of a line can be represented in the form y = mx + b, where m is the slope and b is the y-intercept. In this case, the slope is -2/3 and the line passes through the point (6, 1). By substituting the values into the equation, we can solve for the y-intercept. Thus, the equation of the line is y = -2/3x + 5.
15.
What is the formula for Point-Slope Form?
Correct Answer
A. Y-y1=m(x-x1)
Explanation
The formula for Point-Slope Form is y-y1=m(x-x1). This formula represents a linear equation in the form of y = mx + b, where m is the slope of the line and (x1, y1) are the coordinates of a point on the line. By substituting these values into the equation, we can determine the equation of a line given its slope and a point on the line.
16.
What is the equation of the line that has a slope of 1/4 and passes through the point (5, -2)?
Correct Answer
C. Y = 1/4x - 13/4
Explanation
The equation of a line can be written in the form y = mx + b, where m is the slope and b is the y-intercept. In this case, the slope is given as 1/4. The line passes through the point (5, -2), which means that when x = 5, y = -2. Plugging these values into the equation, we get -2 = (1/4)(5) + b. Solving for b, we find that b = -13/4. Therefore, the equation of the line is y = 1/4x - 13/4.
17.
What is the equation of the line that has a slope of -4/7 and passes through the point (0, -3)?
Correct Answer
A. Y = -4/7x - 3
Explanation
The equation of a line can be represented in the form y = mx + b, where m is the slope and b is the y-intercept. In this case, the slope is -4/7, so the equation starts with y = -4/7x. The line passes through the point (0, -3), which means that when x = 0, y = -3. Plugging these values into the equation, we get -3 = -4/7(0), which simplifies to -3 = 0. Therefore, the y-intercept is -3. Combining the slope and y-intercept, we get the equation y = -4/7x - 3.
18.
Write the equation of the line perpendicular to the line y = 3/4x + 1 through the point (3, 2).
Correct Answer
B. Y = -4/3x + 6
Explanation
The equation of a line perpendicular to y = 3/4x + 1 will have a slope that is the negative reciprocal of 3/4. The negative reciprocal of 3/4 is -4/3. Therefore, the equation of the line perpendicular to y = 3/4x + 1 will be y = -4/3x + b, where b is the y-intercept. To find the value of b, we can substitute the coordinates of the point (3,2) into the equation. Plugging in the values, we get 2 = -4/3(3) + b. Solving for b, we find that b = 6. Therefore, the equation of the line perpendicular to y = 3/4x + 1 through the point (3,2) is y = -4/3x + 6.
19.
Which of the following lines is parallel to the line y = 4x + 1
Correct Answer
D. Y = 4x - 1
Explanation
The given line y = 4x + 1 has a slope of 4. In order for a line to be parallel to this line, it must have the same slope of 4. The line y = 4x - 1 has a slope of 4, making it parallel to the given line.
20.
Which of the following lines is perpendicular to the liney = 4x + 1
Correct Answer
C. Y = -(1/4)x + 1
Explanation
The line y = -(1/4)x + 1 is perpendicular to the line y = 4x + 1 because the slopes of perpendicular lines are negative reciprocals of each other. The slope of y = 4x + 1 is 4, so the slope of the perpendicular line must be -1/4. Additionally, both lines have a y-intercept of 1, which is consistent with the given equation y = -(1/4)x + 1. Therefore, y = -(1/4)x + 1 is the line that is perpendicular to y = 4x + 1.
21.
Which of the following points lies on the liney - 5 = 3(x - 7)
Correct Answer
A. (-5, -7)
Explanation
The equation y - 5 = 3(x - 7) represents a line in slope-intercept form, where the slope is 3 and the y-intercept is (7, 5). To check if a point lies on this line, we substitute the x and y coordinates of the point into the equation and see if it holds true. For the point (-5, -7), substituting these values into the equation gives -7 - 5 = 3(-5 - 7), which simplifies to -12 = -36. Since this equation is true, the point (-5, -7) lies on the line.
22.
If two line contain the same slope and different y-intercepts, then:
Correct Answer
B. The lines will never intersect.
Explanation
When two lines have the same slope but different y-intercepts, they are parallel to each other. Parallel lines never intersect, as they maintain a constant distance between each other. Therefore, the correct answer is that the lines will never intersect.
23.
A line contains point (2,6) and (4, -2). Find the equation of the line in the point-slope form.
Choose all that apply:
Correct Answer(s)
A. Y - 6 = -4 (x - 2)
C. Y + 2 = -4 (x - 4)
Explanation
The point-slope form of a linear equation is given by y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope of the line.
Given the points (2,6) and (4,-2), we can calculate the slope as (change in y) / (change in x) = (-2 - 6) / (4 - 2) = -8 / 2 = -4.
Using the point-slope form, we can substitute the values of (x1, y1) = (2, 6) and m = -4 into the equation to get y - 6 = -4(x - 2), which is equivalent to y - 6 = -4x + 8.
Similarly, substituting the values of (x1, y1) = (4, -2) and m = -4, we get y + 2 = -4(x - 4), which is equivalent to y + 2 = -4x + 16.
Therefore, the correct answers are y - 6 = -4(x - 2) and y + 2 = -4(x - 4).