1.
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 should be -(1/4). Additionally, both lines have a y-intercept of 1, so they are parallel on the y-axis. Therefore, y = -(1/4)x + 1 is the correct answer.
2.
Which of the following lines is parallel to the line y = 4x + 1
Correct Answer
D. Y = 4x - 1
Explanation
The line y = 4x - 1 is parallel to the line y = 4x + 1 because both lines have the same slope of 4. The y-intercept of the line y = 4x - 1 is -1, which is different from the y-intercept of the line y = 4x + 1, but this does not affect the parallelism of the lines.
3.
Which of the following lines is perpendicular to y - 8 = -5 (x + 3)
Correct Answer
D. 7x - 35y = -9
Explanation
The line 7x - 35y = -9 is perpendicular to the given line y - 8 = -5 (x + 3) because the slopes of the two lines are negative reciprocals of each other. The given line has a slope of -5, so the perpendicular line must have a slope of 1/5. The equation 7x - 35y = -9 can be rewritten as y = (7/35)x + (9/35), which simplifies to y = (1/5)x - (9/35). Therefore, the line 7x - 35y = -9 is perpendicular to y - 8 = -5 (x + 3).
4.
Which of the following lines is perpendicular to y - 5 = 1/7 (x + -9)
Correct Answer
B. Y = -7x + 16
Explanation
The given equation of the line is in the slope-intercept form, y = mx + b, where m is the slope of the line. Perpendicular lines have slopes that are negative reciprocals of each other. The slope of the given line is 7, so the slope of the line perpendicular to it would be -1/7. The equation y = -7x + 16 has a slope of -7, which is the negative reciprocal of 7, making it perpendicular to the given line. Therefore, y = -7x + 16 is the line that is perpendicular to y - 5 = 1/7 (x + -9).
5.
A line parallel to 8x - 4y = 9 will have a slope of ___________
Correct Answer
2
m = 2
m=2
Explanation
The given equation is in the form of Ax + By = C, where A = 8, B = -4, and C = 9. To find the slope of a line parallel to this equation, we need to find the slope of the given equation. The slope of a line in this form can be found by rearranging the equation to the slope-intercept form y = mx + b, where m is the slope. By rearranging the given equation, we get y = 2x - (9/4). Therefore, the slope of the given equation is 2. Since lines that are parallel have the same slope, a line parallel to 8x - 4y = 9 will also have a slope of 2.
6.
A line parallel to (y + 7) = -4 ( x - 5) will have a slope of ___________
Correct Answer
-4
m = -4
m=-4
Explanation
The given equation is in the form y = mx + c, where m is the slope of the line. In this equation, the slope is -4. Therefore, any line parallel to this line will also have a slope of -4.
7.
A line perpendicular to 8x - 4y = 9 will have a slope of ___________
Correct Answer
-1/2
Explanation
To find the slope of a line perpendicular to a given line, we need to find the negative reciprocal of the slope of the given line. The given line is in the form of y = mx + b, where m is the slope. By rearranging the equation 8x - 4y = 9 to the slope-intercept form, we get y = 2x - 9/4. Comparing this equation with y = mx + b, we can see that the slope of the given line is 2. Therefore, the slope of a line perpendicular to it would be the negative reciprocal of 2, which is -1/2.
8.
A line perpendicular to 8x + 7y = -15 will have a slope of ___________
Correct Answer
7/8
m = 7/8
m=7/8
Explanation
The given equation is in the form of Ax + By = C, where A = 8, B = 7, and C = -15. To find the slope of a line perpendicular to this equation, we need to find the negative reciprocal of the slope of the given line. The slope of the given line can be found by rearranging the equation in the form y = mx + b, where m represents the slope. In this case, the slope is -A/B, which is -8/7. The negative reciprocal of -8/7 is 7/8, which represents the slope of the line perpendicular to the given equation. Therefore, the correct answer is 7/8.
9.
A line perpendicular to (y + 2) = -3 ( x + 7) will have a slope of ___________
Correct Answer
1/3
m = 1/3
Explanation
A line perpendicular to a given line will have a slope that is the negative reciprocal of the slope of the given line. In the equation (y + 2) = -3 ( x + 7), the slope is -3. The negative reciprocal of -3 is 1/3. Therefore, a line perpendicular to this given line will have a slope of 1/3.
10.
Which of the following lines is parallel to 8x - 5y = -2
Correct Answer
C. Y - 6 = 8/5 (x + 6)
Explanation
The given equation 8x - 5y = -2 is in the form of Ax + By = C, where A = 8, B = -5, and C = -2. To find a line parallel to this equation, we need to find another equation with the same slope. The slope of the given equation can be found by rearranging it into slope-intercept form (y = mx + b), where m is the slope. Rearranging 8x - 5y = -2, we get y = (8/5)x + 2/5. Therefore, any equation with a slope of 8/5 will be parallel to the given equation. The equation y - 6 = 8/5 (x + 6) has the same slope of 8/5, so it is parallel to the given equation.