Problem 1 :
Find the slope of a straight joining the two points (3, -2) and (-1, 4).
Problem 2 :
Find the slope of a straight joining the two points (5, -2) and (4, -1).
Problem 3 :
Find the slope of a straight joining the two points (-2, -1) and (4, 0).
Problem 4 :
Find the slope of a straight joining the two points (1, 2) and (-4, 5).
Problem 5 :
If the slope of a line joining the two points (1, -2) and (3, k) is 5, find the value of k.
Problem 6 :
If the line that passes through (4, 3) and (-5, r) has a slope of -1, what is the value of r?
Problem 7 :
If the line that passes through (a, 7) and (1, a) has a slope of -⁵⁄₉, what is the value of a?
Problem 8 :
The graph of the linear function f passes through the points (a, 1) and (1, b) in the xy-plane. If the slope of the graph of f is 1, which of the following is true?
(A) a - b = 1
(B) a + b = 1
(C) a - b = 2
(D) a + b = 2
Problem 9 :
Find the slope of the line in xy-plane shown below.
Problem 10 :
Find the slope of the line in xy-plane shown below.
1. Answer :
(3, -2) and (-1, 4)
Formula to find the slope of a line joining two points :
Substitute (x_{1}, y_{1}) = (3, -2) and (x_{2}, y_{2}) = (-1, 4).
2. Answer :
(5, -2) and (4, -1)
Formula :
Substitute (x_{1}, y_{1}) = (5, -2) and (x_{2}, y_{2}) = (4, -1).
m = -1
3. Answer :
(-2, - 1) and (4, 0)
Formula :
Substitute (x_{1}, y_{1}) = (-2, -1) and (x_{2}, y_{2}) = (4, 0).
4. Answer :
(1, 2) and (-4, 5)
Formula :
Substitute (x_{1}, y_{1}) = (1, 2) and (x_{2}, y_{2}) = (-4, 5).
5. Answer :
slope = 5
Substitute (x_{1}, y_{1}) = (1, -2) and (x_{2}, y_{2}) = (3, k).
Multiply both sides by 2.
k + 2 = 10
Subtract 2 from both sides.
k = 8
6. Answer :
slope = -1
Substitute (x_{1}, y_{1}) = (4, 3) and (x_{2}, y_{2}) = (-5, r).
Multiply both sides by -9.
r - 3 = 9
Add 3 to both sides.
r = 12
7. Answer :
Substitute (x_{1}, y_{1}) = (a, 7) and (x_{2}, y_{2}) = (1, a).
By cross-multiplication,
9(a - 7) = -5(1 - a)
Use the Distributive Property.
9a - 63 = -5 + 5a
Subtract 5a from both sides.
4a - 63 = -5
Add 63 to both sides.
4a = 58
Divide both sides by 4.
a = ⁵⁸⁄₄
a = ²⁹⁄₂
8. Answer :
slope = 1
Substitute (x_{1}, y_{1}) = (a, 1) and (x_{2}, y_{2}) = (1, b).
Multiply both sides by (1 - a).
b - 1 = 1 - a
Add a to both sides.
a + b - 1 = 1
Add 1 to both sides.
a + b = 2
Therefore, the corect answer is option (D).
9. Answer :
Measure the rise and run.
For the above line,
rise = -4
run = 3
Then,
slope = ʳⁱˢᵉ⁄ᵣᵤₙ
= -⁴⁄₃
10. Answer :
Measure the rise and run.
For the above line,
rise = 6
run = 9
Then,
slope = ʳⁱˢᵉ⁄ᵣᵤₙ
= ⁶⁄₉
= ⅔
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