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Video Questions and Answers on Equations of Straight Lines
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)
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1.
A perpendicular is drawn from a point (3,5) to the line 2y+x=3.Find the equation of the perpendicular.
2.
A perpendicular to the line y - 4x + 3=0 passes through the point (-8,5).Determine its equation.
3.
The equation of a line is
-
3
5
x
+
3
y
=
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.
4.
Find the equation of the perpendicular to the line x+2y=4 and passes through point (2,1)
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
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
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.
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
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.
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
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.
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)
13.
A line passes through points (3,5) and (2,3).Find the equation of the line
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
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
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
17.
A perpendicular is drawn from a point (3,6) to the line 3y+x=6. Find the equation of the perpendicular
18.
Find the equation of the perpendicular to the line 2x+4y=10 and passes through point (4,1)
19.
X(3,-1) and Y(-2,-4) are points on a straight line. Find the equation of XY
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.
21.
In the figure below, name the lines whose gradient is: (a) positive (b) negative (c) zero (d) undefined
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)
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)
24.
Find the gradients of the lines marked
l
1
,
l
2
and
l
3
in the figure below.
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
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
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)
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)
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.
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)
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)
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
)
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)
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.
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
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
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
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.
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)
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)
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.
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.
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.
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.
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
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