# Video Questions and Answers on Equations of Straight Lines

Video Questions and Answers on Equations of Straight Lines.

In this course, we are going to solve several questions on Equations of Straight Lines.

Lessons (**45**) * SHARE*

- 1.
A perpendicular is drawn from a point (3,5) to the line 2y+x=3.Find the equation of the perpendicular.

9m 33s - 2.
A perpendicular to the line y - 4x + 3=0 passes through the point (-8,5).Determine its equation.

8m 17s - 3.
The equation of a line is #- 3/5 x+3y=6#. Find the: (a) The gradient of the line (b)Equation of a line passing through point (1,2) and perpendicular to the given line.

8m 35s - 4.
Find the equation of the perpendicular to the line x+2y=4 and passes through point (2,1)

5m 51s - 5.
A straight line passes through points A(-3,8) and B(3,-4).Find the equation of the straight line through (3,4) and parallel to AB. Give the answer in the form y=mx+c where m and c are constants

6m 9s - 6.
P (5,-4) and Q (-1,-2) are points on a straight line. Find the equation of the perpendicular bisector of PQ; giving the answer in the form y=mx+c

8m 37s - 7.
A line with gradient of -3 passes through the points (3,k) and (k,8).Find the value of k and hence express the equation of the line in the form of ax+ay=c ,where a, b and c constants.

9m 44s - 8.
The equation of line #L_1# is 2y-5x-8=0 and line #L_2# , passes through the points (-5,0) and (5,-4).Without drawing the lines #L_1# and #L_2#, show that the two lines are perpendicular

6m 9s - 9.
A line which joins the points A(3,k) and B(-2,5) is parallel to another line whose equation is 5y+2x=10.Find the value of k.

4m 4s - 10.
A straight line l passes through the point (3,-2) and is perpendicular to a line whose equation is 2y-4x=1.Find the equation of l in the form y=mx+c, where m and c are constants

0m 0s - 11.
A line L passes through point (3,1) and is perpendicular to the line 2y=4x+5. Determine the equation of the line L.

4m 7s - 12.
A straight line passes through points (-2,1) and (6,3).
Find:
a) The equation of the line in the form of y=mx+c ;
b)The gradient of a line perpendicular to the line in (a)

5m 24s - 13.
A line passes through points (3,5) and (2,3).Find the equation of the line

2m 41s - 14.
A line L is perpendicular to the line #2/3 x + 5/7 y=1# Given that L passes through (4,11) find : a) Gradient of L
b) Equation of L in the form y=mx+c, where m and c are constants

10m 24s - 15.
Two vertices of a triangle ABC are A (3,6) and B(7,12).
a) Find the equation of line AB
b) Find the equation of the perpendicular bisector of line AB

8m 40s - 16.
a) A line #L_1# passes through point (3,3) and (5,7).Find the equation of #L_1# in the form of y=mx+c, where m and c are constants
b) Another line #L_2# is perpendicular to #L_1# and passes through (-2,3).Find i) The equation of #L_2#
ii) The x-intercept of #L_2#

7m 48s - 17.
A perpendicular is drawn from a point (3,6) to the line 3y+x=6. Find the equation of the perpendicular

3m 27s - 18.
Find the equation of the perpendicular to the line 2x+4y=10 and passes through point (4,1)

3m 21s - 19.
X(3,-1) and Y(-2,-4) are points on a straight line. Find the equation of XY

3m 37s - 20.
The equations of two sides of a parallelogram are y=-2 and y=x-2. If one of the vertices of the parallelogram has co-ordinates (14, 5), find the equations of the other two sides and the remaining vertices.

3m 56s - 21.
In the figure below, name the lines whose gradient is:
(a) positive (b) negative (c) zero (d) undefined

5m 44s - 22.
For each of the following pairs of points, find the gradients of the lines passing through them:
(a) A(2, 3), B(5, 6)
(b) C(5, 10), D(12, 20)
(c) E(-5, 6), F(2, 1)
(d) G(4, 5), H(6, 5)
(e) I(8, 0), J(12, -6)

2m 5s - 23.
For each of the following pairs of points, find the gradients of the lines passing through them.
(a) K(5, -2), L(6, 2)
(b) M(6, 3), N(-6, +2)
(c) P(2, -5), Q(2, 3)
(d) R(1/4,1/3), S(1/3,1/4)
(e) T(0.5, 0.3), U(-0.2, -0.7)

2m 49s - 24.
Find the gradients of the lines marked # l_1, l_2# and #l_3#in the figure below.

3m 52s - 25.
For each of the following straight lines, determine the gradient and the y-intercept without drawing the line:
(a) 3y = 7x
(b) 2y = 6x + 1
(c) 7 - 2x = 4y
(d) 3y = 7
(e) 2y - 3x + 4 = 0
(f) 3(2x - 1) = 5y
(g) y + 3x + 7 = 0

4m 21s - 26.
For each of the following straight lines, determine the gradient and the y-intercept without drawing the line.
(a) 5x - 3y + 6 = 0
(b) #3/2# y - 15 = #2/3#x
(c) 2(x + y) = 4
(d) #1/3#x + #2/5#y + #1/6# = 0
(e) -10(x +3) = 0.5y
(f) ax + by + c = 0

5m 52s - 27.
Find the equations of the lines with the given gradients and passing through the given points:
(a) 4; (2, 5)
(b) #3/4#; (-1, 3)
(c) -2; (7, 2)
(d) #-1/3#; (6, 2)

3m 52s - 28.
Find the equations of the lines with the given gradients and passing through the given points:
(a) 0; (-3, -5)
(b) #-3/2#; (0, 7)
(c) m; (1, 2)
(d) m; a, b)

3m 0s - 29.
Write the equations of the lines #l_1, l_2, l_3, l_4# shown in the figure below in the form y = mx + c.

7m 57s - 30.
Find the equation of the line passing through the given points:
(a) (0, 0) and (1, 3)
(b) (0, -4) and (1, 2)
(c) (0, 4) and (-1, -2)
(d) (1, 0) and (3, -3)
(e) (3, 7) and (5, 7)

4m 7s - 31.
Find the co-ordinates of the point where each of the following lines cuts the x-axis:
(a) y = 7x - 3
(b) y = -(3x + 2)
(c) y = #1/3#x + 4
(d) y = 0.5 - 0.8x
(e) y = mx + c
(f) ax+by+c= 0 (a#!=# 0)

3m 54s - 32.
Find the equation of the line passing through the given points.
(a) (-1, 7) and (3, 3)
(b) (11, 1) and (14, 4)
(c) (5, -2.5) and (3.5, -2)
(d) (a, b) and (c, d)
(e) (#x_1#,#y_1#) and (#x_2#,# y_2#)

7m 30s - 33.
The x and y-intercepts of a line are given below. Determine the equation of the line in each case:
x-intercept y-intercept
(a) -2 -2
(b) -3 4
(c) 5 -1
(d) 3 4
(e) a b(a#!=# 0, b#!=# 0)

4m 37s - 34.
The equation of the base of an isosceles triangle ABC is y = -2 and the equation of one of its sides is y + 2x = 4. If the co-ordinates of A are (-1, 6), find the co-ordinates of B and C. Hence, find the equation of the remaining side.

4m 56s - 35.
Draw the lines passing through the given points and having the given gradients:
(a) (0, 3); 3
(b) (0, 2); 5
(c) (4, 3); 2

8m 13s - 36.
Draw the graphs of the following lines using the x and y-intercepts:
(a) y = #1/2#x + 3
(b) 3y - 4x = 5
(c) y + 2x – 3 = 0
(d) y = –2x + 2

3m 11s - 37.
Without drawing, determine which of the following pairs of lines are perpendicular:
(a) y = 2x + 7
y= -#1/2#x+3
(b) 3y = x + 3
y = –3x – 2
(c) y = 2x + 71
y =-2x+5
(d) y = 5x + 1
5y =10 – x

3m 17s - 38.
Without drawing, determine which of the following pairs of lines are perpendicular.
(a) y= 3x– 1
y = #3/2#x - 4
(b) y = #2/3#x + 4
2y+3x=8
(c) 2y – 7x = 4
y= #2/7#x - #1/2#
(d) y= -#3/4#x - 2
y= -#4/3#x + 5.

3m 19s - 39.
Determine the equations of the lines perpendicular to the given lines and passing through the given points:
(a) y – 5x + 3 = 0; (3, 2)
(b) y = 8 – 7x; (–3, –4)
(c) y + 3x + 5 = 0; (0.25, –0.75)

5m 26s - 40.
Determine the equations of the lines perpendicular to the given lines and passing through the given points:
(a) y + x = 17; (– 4, 2)
(b) y = 17; (–2, –1)
(c) y = mx + c; (a, b)

4m 17s - 41.
A triangle has vertices A(2, 5), B(1, –2) and C(–5, 1). Determine:
(a) the equation of the line BC.
(b) the equation of the perpendicular line from A to BC.

4m 0s - 42.
ABCD is a rhombus. Three of its vertices are A(1, 2), B(4, 6) and C(4, 11). Find the equations of its diagonals and the co-ordinates of vertex D.

4m 20s - 43.
The point D(-2, 5) is one of the vertices of a square ABCD. The equations of the lines AB and AC are y = #1/3#x - 1 and y = 2x - 1 respectively. Determine the equations of sides DA, DB and DC. Hence, find the co-ordinates of the remaining three vertices.

15m 30s - 44.
ABCD is a rectangle with the centre at the origin. A is the point (5, 0). Points B and C lie on the line 2y = x + 5. Determine the co-ordinates of the other vertices.

6m 4s - 45.
In each of the following, find the equation of the line through the give point and parallel to the given line:
(a) (-#7/3#,#3/4#); 2(y-2x) = 1.1
(b) (3#1/7#, -1#1/7#); 15(1-x) = 22y
(c) (-3, 4); x = 101

4m 0s

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