Straight lines
Q. Determine the equation of the line that passes through the points (0, 0) and (3, 9).
A.
y = 3x
B.
y = 2x
C.
y = 3x + 1
D.
y = x + 1
Show solution
Solution
The slope m = (9 - 0) / (3 - 0) = 3. The equation is y = 3x.
Correct Answer: A — y = 3x
Learn More →
Q. Determine the point of intersection of the lines y = 2x + 1 and y = -x + 4.
A.
(1, 3)
B.
(2, 5)
C.
(3, 7)
D.
(4, 9)
Show solution
Solution
Setting 2x + 1 = -x + 4 gives 3x = 3, hence x = 1. Substituting back gives y = 3.
Correct Answer: A — (1, 3)
Learn More →
Q. Determine the x-intercept of the line 4x - 2y + 8 = 0.
Show solution
Solution
Setting y = 0 in the equation gives 4x + 8 = 0, thus x = -2.
Correct Answer: B — 2
Learn More →
Q. Determine the x-intercept of the line 4x - 5y + 20 = 0.
Show solution
Solution
Setting y = 0 in the equation gives 4x + 20 = 0, thus x = -5.
Correct Answer: D — -4
Learn More →
Q. Determine the x-intercept of the line 5x + 2y - 10 = 0.
Show solution
Solution
Setting y = 0 in the equation gives 5x - 10 = 0, thus x = 2.
Correct Answer: B — 5
Learn More →
Q. Determine the x-intercept of the line given by the equation 2x - 3y + 6 = 0.
Show solution
Solution
Set y = 0 in the equation: 2x + 6 = 0 => x = -3.
Correct Answer: B — 3
Learn More →
Q. Find the angle between the lines y = 2x + 1 and y = -0.5x + 3.
A.
60 degrees
B.
45 degrees
C.
90 degrees
D.
30 degrees
Show solution
Solution
The slopes are m1 = 2 and m2 = -0.5. The angle θ is given by tan(θ) = |(m1 - m2) / (1 + m1*m2)| = |(2 + 0.5) / (1 - 1)|, which is undefined, indicating 90 degrees.
Correct Answer: A — 60 degrees
Learn More →
Q. Find the distance from the point (1, 2) to the line 3x + 4y - 12 = 0.
Show solution
Solution
Distance = |Ax1 + By1 + C| / sqrt(A^2 + B^2) = |3(1) + 4(2) - 12| / sqrt(3^2 + 4^2) = |3 + 8 - 12| / 5 = 1.
Correct Answer: A — 2
Learn More →
Q. Find the distance from the point (3, 4) to the line 2x + 3y - 6 = 0.
Show solution
Solution
Distance = |Ax1 + By1 + C| / sqrt(A^2 + B^2) = |2*3 + 3*4 - 6| / sqrt(2^2 + 3^2) = |6 + 12 - 6| / sqrt(13) = 12 / sqrt(13).
Correct Answer: B — 3
Learn More →
Q. Find the equation of the line passing through the points (1, 2) and (3, 4).
A.
y = x + 1
B.
y = 2x
C.
y = x + 3
D.
y = 2x - 1
Show solution
Solution
The slope m = (4-2)/(3-1) = 1. Using point-slope form: y - 2 = 1(x - 1) gives y = x + 1.
Correct Answer: A — y = x + 1
Learn More →
Q. Find the equation of the line that is perpendicular to y = 5x + 2 and passes through (2, 3).
A.
y = -1/5x + 4
B.
y = 5x - 7
C.
y = -5x + 13
D.
y = 1/5x + 2
Show solution
Solution
The slope of the perpendicular line is -1/5. Using point-slope form: y - 3 = -1/5(x - 2) gives y = -1/5x + 13/5.
Correct Answer: C — y = -5x + 13
Learn More →
Q. Find the equation of the line that is perpendicular to y = 5x + 2 and passes through the origin.
A.
y = -1/5x
B.
y = 5x
C.
y = -5x
D.
y = 1/5x
Show solution
Solution
The slope of the given line is 5. The slope of the perpendicular line is -1/5. Using y = mx + c, we get y = -1/5x.
Correct Answer: C — y = -5x
Learn More →
Q. Find the equation of the line that passes through the origin and has a slope of -2.
A.
y = -2x
B.
y = 2x
C.
y = -x
D.
y = x
Show solution
Solution
Using the slope-intercept form: y = mx + b, where b = 0, we have y = -2x.
Correct Answer: A — y = -2x
Learn More →
Q. Find the midpoint of the line segment joining the points (2, 3) and (4, 7).
A.
(3, 5)
B.
(2, 5)
C.
(4, 3)
D.
(5, 6)
Show solution
Solution
Midpoint M = ((x1 + x2)/2, (y1 + y2)/2) = ((2 + 4)/2, (3 + 7)/2) = (3, 5).
Correct Answer: A — (3, 5)
Learn More →
Q. Find the point of intersection of the lines y = 2x + 1 and y = -x + 4.
A.
(1, 3)
B.
(2, 5)
C.
(3, 7)
D.
(4, 9)
Show solution
Solution
Setting 2x + 1 = -x + 4 gives 3x = 3, thus x = 1. Substituting x back gives y = 3, so the point is (1, 3).
Correct Answer: A — (1, 3)
Learn More →
Q. Find the point of intersection of the lines y = x + 1 and y = -x + 5.
A.
(2, 3)
B.
(3, 2)
C.
(1, 2)
D.
(0, 1)
Show solution
Solution
Set x + 1 = -x + 5. Solving gives x = 2, y = 3. Thus, the point is (2, 3).
Correct Answer: A — (2, 3)
Learn More →
Q. Find the slope of the line passing through the points (2, 3) and (4, 7).
Show solution
Solution
The slope m is given by (y2 - y1) / (x2 - x1) = (7 - 3) / (4 - 2) = 4 / 2 = 2.
Correct Answer: A — 2
Learn More →
Q. Find the slope of the line that passes through the points (0, 0) and (5, 5).
Show solution
Solution
The slope m = (5 - 0) / (5 - 0) = 1.
Correct Answer: B — 1
Learn More →
Q. Find the y-intercept of the line represented by the equation 5x - 2y = 10.
Show solution
Solution
Set x = 0: -2y = 10 => y = -5. The y-intercept is (0, -5).
Correct Answer: B — 2
Learn More →
Q. If a line passes through the points (1, 1) and (2, 3), what is its equation in slope-intercept form?
A.
y = 2x - 1
B.
y = 3x - 2
C.
y = 2x + 1
D.
y = x + 2
Show solution
Solution
Slope m = (3 - 1) / (2 - 1) = 2. Using point-slope form: y - 1 = 2(x - 1) => y = 2x - 1.
Correct Answer: A — y = 2x - 1
Learn More →
Q. If the line 3x + 4y = 12 intersects the x-axis, what is the point of intersection?
A.
(4, 0)
B.
(0, 3)
C.
(0, 4)
D.
(3, 0)
Show solution
Solution
Set y = 0 in the equation: 3x = 12 => x = 4. The point is (4, 0).
Correct Answer: A — (4, 0)
Learn More →
Q. If the line 3x + 4y = 12 is transformed to slope-intercept form, what is the slope?
A.
-3/4
B.
3/4
C.
4/3
D.
-4/3
Show solution
Solution
Rearranging gives y = -3/4x + 3. The slope is -3/4.
Correct Answer: A — -3/4
Learn More →
Q. If the line 3x + 4y = 12 is transformed to slope-intercept form, what is the y-intercept?
Show solution
Solution
Rearranging gives y = -3/4x + 3. The y-intercept is 3.
Correct Answer: B — 4
Learn More →
Q. If the line 3x - 4y + 12 = 0 is parallel to another line, what is the slope of that line?
A.
3/4
B.
-3/4
C.
4/3
D.
-4/3
Show solution
Solution
The slope of the line is given by -A/B = -3/-4 = 3/4. Parallel lines have the same slope.
Correct Answer: B — -3/4
Learn More →
Q. If the line 3x - 4y + 12 = 0 is transformed to slope-intercept form, what is the slope?
A.
3/4
B.
-3/4
C.
4/3
D.
-4/3
Show solution
Solution
Rearranging gives y = (3/4)x + 3, so the slope is -3/4.
Correct Answer: B — -3/4
Learn More →
Q. If the line 5x + 12y = 60 is transformed to slope-intercept form, what is the slope?
A.
-5/12
B.
5/12
C.
12/5
D.
-12/5
Show solution
Solution
Rearranging gives y = -5/12 x + 5, so the slope is -5/12.
Correct Answer: A — -5/12
Learn More →
Q. If the line 5x + 2y = 10 intersects the y-axis, what is the y-coordinate of the intersection point?
Show solution
Solution
Setting x = 0 in the equation gives 2y = 10, hence y = 5.
Correct Answer: B — 2
Learn More →
Q. If the line 5x - 2y + 10 = 0 is reflected about the x-axis, what is the new equation?
A.
5x + 2y + 10 = 0
B.
5x - 2y - 10 = 0
C.
5x + 2y - 10 = 0
D.
5x - 2y + 10 = 0
Show solution
Solution
Reflecting about the x-axis changes the sign of y-coefficient: 5x + 2y + 10 = 0.
Correct Answer: A — 5x + 2y + 10 = 0
Learn More →
Q. What is the angle between the lines 2x + 3y - 6 = 0 and 4x - y + 1 = 0?
A.
45 degrees
B.
60 degrees
C.
90 degrees
D.
30 degrees
Show solution
Solution
The slopes of the lines are -2/3 and 4. The angle θ can be found using tan(θ) = |(m1 - m2) / (1 + m1*m2)|.
Correct Answer: C — 90 degrees
Learn More →
Q. What is the angle between the lines y = 2x + 1 and y = -0.5x + 3?
A.
90 degrees
B.
60 degrees
C.
45 degrees
D.
30 degrees
Show solution
Solution
The slopes are m1 = 2 and m2 = -0.5. The angle θ is given by tan(θ) = |(m1 - m2) / (1 + m1*m2)| = |(2 + 0.5) / (1 - 1)|, which is undefined, indicating 90 degrees.
Correct Answer: A — 90 degrees
Learn More →
Showing 1 to 30 of 56 (2 Pages)
