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Slope of the Line Equation Worksheet

Slope of the Line Equation Worksheet
  • Page 1
 1.  
If A = (4, 3), B = (5, 4) and C = (8, 7), then which of the following is correct?
a.
Triangle ABC is equilateral triangle
b.
Triangle ABC is right triangle
c.
Triangle ABC is scalane triangle
d.
A, B, and C are collinear


Solution:

Three points A, B, C are collinear the slope of the line joining A, B = slope of line joining B, C.
[Definition.]

The points are A(4, 3), B(5, 4), C(8, 7)

Slope of line joining A, B = ΔyΔx = 4 - 35 - 4 = 1

Slope of line joining B, C = ΔyΔx = 7 - 48 - 5 = 1

Here slope of line joining A, B = slope of line joining B, C = 1

Hence, the points A, B, C are collinear.


Correct answer : (4)
 2.  
What is the slope of a line on which for every point the x coordinate is same?
a.
Infinitely small
b.
Infinitely large
c.
Undefined


Solution:

Let L be the line on which for every point the x coordinate is same.

So, let A(x, y1), B(x, y2) be two points on line L.

Slope of line L = Slope of line joining A,B = m = ΔyΔx
[Use the slope formula.]

= y2 -y1x - x

= y2 -y10 = Undefined
[Division by 0 is not defined]


Correct answer : (4)
 3.  
Find the slope of the line passing through the points A (7, 9) and B (12, 12).
a.
3 5
b.
19 21
c.
8
d.
- 19 21


Solution:

The slope of the line joining the two points A (7, 9) and B (12, 12) = m = ΔyΔx

= 12 - 912 - 7 = 3 / 5
[Use the slope formula.]


Correct answer : (1)
 4.  
If ab, then what is the slope of the line joining the points P(5a, 6b) and Q(6b, 5a)?
a.
Independent of a, b
b.
Dependent of a
c.
Dependent of a, b
d.
Dependent of b


Solution:

The slope of the line joining the points P(5a, 6b) and Q(6b, 5a) = m = ΔyΔx

m = 5a - 6b6b - 5a
[Use the slope formula.]

= - (5a - 6b5a - 6b)

m = - 1

Slope of the line is "- 1" which is independent of both a, b.


Correct answer : (1)
 5.  
What is the slope of the line on which for every point the ordinate is same?
a.
Undefined
b.
Infinitely large
c.
Infinitely small


Solution:

Let L be the line on which for every point the ordinate is same.

So, let P(x1, y) and Q(x2, y) be the two points on line L.

Slope of line L = Slope of line joining P,Q = m = ΔyΔx

= y - yx2 -x1
[Use the slope formula.]

= 0x2 -x1 = 0


Correct answer : (2)
 6.  
Find the angle of inclination of a line whose slope is 3.
a.
5π4
b.
π4
c.
 π3
d.
2π3


Solution:

Let θ be the angle of inclination of the line with slope (- 3)

tan θ = - 3
[Use the definition of slope.]

tan θ = - 3 = tan(2π3)
[0 ≤ θ < π]

θ = 2π3


Correct answer : (4)
 7.  
If a ≠ - 1, then what is the slope of the line joining the points (- 4a, 4) , (a2 + 4, a2)?
a.
2 - aa + 2
b.
a + 22 - a
c.
a - 2a + 2
d.
a + 2a - 2


Solution:

The two points are P(- 4a, 4 ) and Q(a2 + 4, a2)

Slope of line joining P, Q = m = ΔyΔx = a2 - 4a2 + 4 - (- 4a)
[Use the slope formula.]

m = a2 - 4a2 + 4a +4

= (a - 2)(a + 2)(a + 2)2

= (a - 2)(a + 2)
[Cancel the common factor.]

Slope of line joining P, Q is m = (a - 2)(a + 2)


Correct answer : (3)
 8.  
If t > 1and m is the slope of the line joining the points (2t2 , 4t) and (2t2 , 4t), then which of the following is correct?
a.
m =1
b.
m < 1
c.
m =2
d.
m > 1


Solution:

The points are P(2t2 , 4t)and Q (2t2 , 4t)

Slope of line joining P,Q = m = ΔyΔx = (4t-4t)(2t2-2t2)
[Use the slope formula.]

= 4(t-1t)2(t-1t)(t+1t)

So, m = 2t +1t
[Cancel the common factor.]

2t +1t < 1
[ For t >1, t + 1t > 2.]

So, m < 1.


Correct answer : (2)
 9.  
Find the values of k such that the points (k + 2, 2), (2k + 2, 4) and (2k + 3, 2k + 1) are collinear.
a.
- 12 , 2
b.
- 12 , -2
c.
12 , -2
d.
12 , 2


Solution:

The points are A(k + 2, 2), B(2k + 2, 4) and C(2k + 3, 2k + 1)

Slope of line joining A, B = slope of line joining B,C .
[The three points A, B, C are collinear.]

4 - 22k + 2 - k - 2 = 2k + 1 - 42k + 3 - 2k - 2
[Use the slope formula.]

2k = 2k - 31

2k2 - 3k - 2 = 0

(2k + 1)(k - 2) = 0
[Factor.]

k = - 12 , 2.


Correct answer : (1)
 10.  
What is the slope of the line 3x + 4y + 14 = 0?
a.
- 43
b.
14 3
c.
7 2
d.
- 34


Solution:

Given line is 3x + 4y + 14 = 0

y = (- 34)x + (- 14 / 4)
[Solve for y.]

Slope of the line = m = - 3 / 4
[The above equation is in the slope intercept form y = mx + c. ]


Correct answer : (4)

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