Various forms of equation of a straight line - One Line Questions
1.
In the general form Ax + By + C = 0, the slope of the line is given by: —
-A/B
2.
Convert the equation 3x + 4y = 12 into normal form. —
(3/5)x + (4/5)y = 12/5
3.
The equation of a line passing through (x1, y1) and (x2, y2) can also be written as: —
(x - x1) / (x2 - x1) = (y - y1) / (y2 - y1)
4.
What is the equation of the line that cuts off intercepts of -3 and 4 from the positive axes? —
(x/-3) + (y/4) = 1
5.
Convert the equation 4x - 5y + 20 = 0 into intercept form. —
(x/-5) + (y/4) = 1
6.
The equation of the line joining the points (a, 0) and (0, b) is: —
(x/a) + (y/b) = 1
7.
The two-point form of the equation of a straight line passing through (x1, y1) and (x2, y2) is: —
(y - y1) / (x - x1) = (y2 - y1) / (x2 - x1)
8.
If two lines are perpendicular, the product of their slopes is: —
-1
9.
If A=2, B=3, and C=4 in the equation Ax + By + C = 0, what is the slope of the line? —
-2/3
10.
Find the equation of the line passing through (1, -2) and perpendicular to x - 2y + 5 = 0. —
2x + y - 4 = 0
11.
What is the x-intercept of the line 3x + 4y - 12 = 0? —
4
12.
What is the y-intercept of the line 3x + 4y - 12 = 0? —
3
13.
What is the equation of the line passing through (3, 4) and perpendicular to the line 2x + 3y - 5 = 0? —
3x - 2y + 1 = 0
14.
Find the equation of the line passing through (2, 5) and parallel to 3x + 4y - 7 = 0. —
3x + 4y - 26 = 0
15.
The equation of a line passing through (x1, y1) and parallel to Ax + By + C = 0 is: —
A(x - x1) + B(y - y1) = 0
16.
The equation of a line passing through (x1, y1) and perpendicular to Ax + By + C = 0 is: —
B(x - x1) - A(y - y1) = 0
17.
What is the slope-intercept form of a linear equation? —
y = mx + c
18.
The equation of a line passing through the origin is of the form: —
y = mx
19.
What is the equation of a line parallel to Ax + By + C = 0? —
Ax + By + D = 0
20.
What is the equation of a line perpendicular to Ax + By + C = 0? —
Bx - Ay + D = 0
21.
If two lines are parallel, their slopes are: —
Equal
22.
Which form of the equation of a straight line requires the slope and the y-intercept? —
Slope-intercept form
23.
What form of the equation of a straight line is used when two points on the line are known? —
Two-point form
24.
The equation y - y1 = m(x - x1) represents the equation of a straight line in which form? —
Point-slope form
25.
The equation (x/a) + (y/b) = 1 represents a straight line in which form? —
Intercept form
26.
In the normal form x cos(alpha) + y sin(alpha) = p, 'alpha' represents: —
The angle the normal makes with the x-axis
27.
In the intercept form (x/a) + (y/b) = 1, 'a' and 'b' represent: —
The x-intercept and y-intercept respectively
28.
In the normal form x cos(alpha) + y sin(alpha) = p, 'p' represents: —
The perpendicular distance from the origin to the line
29.
Which form of the equation of a straight line is also known as the symmetric form? —
None of the above
30.
Find the equation of the line passing through (-1, 2) and parallel to the line x - 3y + 4 = 0. —
x - 3y + 7 = 0
31.
The equation of the line passing through the point (0, -3) and parallel to the x-axis is: —
y = -3
32.
The equation of the line passing through the point (5, 0) and parallel to the y-axis is: —
x = 5
33.
The normal form of the equation of a straight line is: —
x cos(alpha) + y sin(alpha) = p
34.
Find the equation of the line passing through (1, 1) and (2, 3). —
y - 1 = (3-1)/(2-1) * (x - 1)
35.
The equation of the line passing through the intersection of 2x + 3y - 7 = 0 and x - y + 1 = 0, and having slope 2 is: —
y - 1 = 2(x - 1)
36.
What is the equation of a line with slope 5 passing through the point (2, 3)? —
y - 3 = 5(x - 2)
37.
What is the equation of the line passing through (2, 3) and having an inclination of 60 degrees? —
y - 3 = sqrt(3)(x - 2)
38.
The equation of the line passing through (a, b) with slope m is: —
y - b = m(x - a)
39.
What is the equation of the line passing through (2, -1) with slope 3? —
y - (-1) = 3(x - 2)
40.
The equation of the line passing through the origin and making an angle of 150 degrees with the positive x-axis is: —
y = -(1/sqrt(3))x
41.
What is the equation of the line passing through the origin and the point (4, 6)? —
y = (3/2)x
42.
The equation of the line passing through the origin and having slope 7 is: —
y = 7x
43.
A vertical line has the equation: —
x = c
44.
A horizontal line has the equation: —
y = c
45.
If a line passes through a single point (x1, y1) and has a slope 'm', its equation is given by: —
y - y1 = m(x - x1)
46.
If a line makes intercepts 'a' on the x-axis and 'b' on the y-axis, its equation is: —
(x/a) + (y/b) = 1
47.
The general form of the equation of a straight line is: —
Ax + By + C = 0
48.
A line passing through the origin (0,0) with slope 'm' has the equation: —
Both B and C
49.
The equation of a line with inclination 45 degrees and passing through (0, 0) is: —
y = x
50.
The equation of a line with inclination 135 degrees and passing through (0, 0) is: —
y = -x