The editorial team at ProProfs Quizzes consists of a select group of subject experts, trivia writers, and quiz masters who have authored over 10,000 quizzes taken by more than 100 million users. This team includes our in-house seasoned quiz moderators and subject matter experts. Our editorial experts, spread across the world, are rigorously trained using our comprehensive guidelines to ensure that you receive the highest quality quizzes.
Write the equation in slope-Intercept form of the line that passes through the point (4,-6) and has a slope of -3/4?
Correct Answer y = -3/4x - 3, y=-3/4x-3
Explanation The equation is in slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept. In this case, the slope is -3/4 and the point (4, -6) lies on the line. We can use the point-slope formula to find the equation: y - y1 = m(x - x1). Substituting the values, we get y - (-6) = (-3/4)(x - 4), which simplifies to y + 6 = (-3/4)x + 3. Rearranging the equation, we get y = (-3/4)x - 3, which matches the given answer.
Rate this question:
2.
Write the equation in slope-intercept form for the equation of the line that passes through the point (-5, -3/4) and has a slope of 1/20 ?
Correct Answer y=1/20x-1/2, y=1/20x-2/4
Explanation The equation in slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept. In this case, the slope is 1/20. To find the y-intercept, we can substitute the coordinates of the given point (-5, -3/4) into the equation and solve for b. By substituting the values, we get -3/4 = (1/20)(-5) + b. Simplifying this equation, we find that b = -1/2. Therefore, the equation in slope-intercept form for the line that passes through the point (-5, -3/4) with a slope of 1/20 is y = 1/20x - 1/2.
Rate this question:
3.
If point (-1,0) is on the line whose equation is y = -2x + b, what is the value of b?
Correct Answer -2, b=-2
Explanation The equation of the line is in the form y = mx + b, where m is the slope and b is the y-intercept. Since the point (-1,0) lies on the line, we can substitute the x and y coordinates into the equation to solve for b. Plugging in x = -1 and y = 0, we get 0 = -2(-1) + b. Simplifying this equation, we get 0 = 2 + b. To isolate b, we subtract 2 from both sides, giving us b = -2. Therefore, the value of b is -2.
Rate this question:
4.
Write the equation of the line that is // to the line y = -1/2x + 4 and passes through the point (-4, -4).Write your answer in slope-intercept form.
Correct Answer y = -1/2x - 6, y=-1/2x-6
Explanation The equation of a line can be written in slope-intercept form as y = mx + b, where m represents the slope and b represents the y-intercept. In this case, the given line is parallel to y = -1/2x + 4, which means it has the same slope of -1/2. Since the line passes through the point (-4, -4), we can substitute these values into the equation and solve for the y-intercept. Plugging in the values, we get -4 = -1/2(-4) + b. Simplifying this equation, we find that b = -6. Therefore, the equation of the line is y = -1/2x - 6.
Rate this question:
5.
Write the equation of the line perpendicular to the line 3x - 5y = -1 and passes through the point ( 3, -4).Write the answer in Standard form.
Correct Answer 5x + 3y = 3, 5x+3y=3
Explanation The equation of a line perpendicular to 3x - 5y = -1 can be found by rearranging the equation into slope-intercept form (y = mx + b), where m is the slope. The slope of the given line is (3/5). The slope of a line perpendicular to this line will be the negative reciprocal of (3/5), which is (-5/3). Using the point-slope form of a line (y - y1 = m(x - x1)), we can substitute the values of the point (3, -4) and the slope (-5/3) to find the equation of the line. Simplifying the equation will give us the standard form: 5x + 3y = 3. Therefore, the correct answer is 5x + 3y = 3.
Rate this question:
6.
Equation 1 has a slope of -2/3, what would be the perpendicular slope for equation 2?
A.
-2/3
B.
2/3
C.
3/2
D.
-3/2
Correct Answer
C. 3/2
Explanation The perpendicular slope for a given slope is the negative reciprocal of that slope. In this case, the given slope is -2/3. To find the perpendicular slope, we take the negative reciprocal of -2/3, which is 3/2. Therefore, the correct answer is 3/2.
Rate this question:
7.
Given the line x = -7/9, what would be slope of the the line perpendicular to this line?
A.
9/7
B.
-7/9
C.
0
D.
Underfined
Correct Answer
C. 0
Explanation The slope of a line perpendicular to another line is the negative reciprocal of the slope of the original line. Since the original line has a slope of 0 (because it is a vertical line), the slope of the line perpendicular to it would be the negative reciprocal of 0, which is also 0.
Rate this question:
8.
The line x = -2 is what type of line
A.
Diagonal line going up
B.
Diagonal line going down
C.
Vertical line
D.
Horizontal line
Correct Answer
C. Vertical line
Explanation The line x = -2 is a vertical line because it is parallel to the y-axis. In a Cartesian coordinate system, a vertical line has a constant x-coordinate and can intersect the y-axis at any point. Since x = -2 is a constant value for all y-values, it represents a vertical line.
Rate this question:
9.
The line x = -2 has what type of slope?
A.
Positive slope
B.
Negative slope
C.
Zero slope
D.
Undefined slope
Correct Answer
D. Undefined slope
Explanation The line x = -2 has an undefined slope because a vertical line does not have a change in y-coordinate for any change in x-coordinate. The slope is typically defined as the change in y divided by the change in x, but since there is no change in x for this line, the slope cannot be calculated. Therefore, the slope is undefined.
Rate this question:
10.
The line 2x - 3y = -1/3 has what type of slope?
A.
Positive Slope
B.
Negative Slope
C.
Zero Slope
D.
Undefined Slope
Correct Answer
A. Positive Slope
Explanation The given equation is in the form y = mx + b, where m represents the slope. In this case, we can rearrange the equation to y = (2/3)x + 1/9. Since the coefficient of x is positive (2/3), the slope is positive. Therefore, the correct answer is positive slope.
Rate this question:
Quiz Review Timeline +
Our quizzes are rigorously reviewed, monitored and continuously updated by our expert board to maintain accuracy, relevance, and timeliness.