CALCULATING SLOPE WORKSHEET

Problem 1 :

Find the slope of a line passing through (3, -9) and (2, -1). 

Problem 2 :

Find the slope of a line passing through (3, 6) and (4, 1). 

Problem 3 :  

Find the slope of a line passing through (7, -3) and (0, -4). 

Problem 4 :

If the slope of a line joining (2, -6) and (8, k) is 2, find the value of k. 

Problem 5 :

If the slope of a line joining (0, k) and (3, -15) is -6, find the value of k. 

Problem 6 :

If the slope of a line joining (k, 3) and (4, 8 ) is 5/6, find the value of k. 

Detailed Answer Key

Problem 1 :

Find the slope of a line passing through (3, -9) and (2, -1). 

Solution :

Formula for slope : 

m  =  (y₂ - y₁) / (x₂ - x₁)

Substitute (x₁, y₁)  =  (3, -9) and (x₂, y₂)  =  (2, -1).  

m  =  [-1 - (-9)] / (2 - 3)

m  =  (-1 + 9) / (2 - 3)

m  =  8 / (-1)

m  =  -8

So, the slope of the line is -8.

Problem 2 :

Find the slope of a line passing through (3, 6) and (4, 1). 

Solution :

Formula for slope : 

m  =  (y₂ - y₁) / (x₂ - x₁)

Substitute (x₁, y₁)  =  (3, 6) and (x₂, y₂)  =  (4, 1).  

m  =  (1 - 6) / (4 - 3)

m  =  (-5) / 1

m  =  -5

So, the slope of the line is -5.

Problem 3 :  

Find the slope of a line passing through (7, -3) and (0, -4). 

Solution :

Formula for slope : 

m  =  (y₂ - y₁) / (x₂ - x₁)

Substitute (x₁, y₁)  =  (7, -3) and (x₂, y₂)  =  (0, -4).  

m  =  [-4 - (-3)] / (0 - 7)

m  =  (-4 + 3) / (-7)

m  =  (-1) / (-7)

m  =  1 / 7

So, the slope of the line is 1/7.

Problem 4 :

If the slope of a line joining (2, -6) and (8, k) is 2, find the value of k. 

Solution :

Formula for slope : 

m  =  (y₂ - y₁) / (x₂ - x₁)

Substitute m  = 2, (x₁, y₁)  =  (2, -6) and (x₂, y₂)  =  (8, k).  

2  =  [k - (-6)] / (8 - 2)

2  =  (k + 6) / 6

Multiply each side by 6. 

12  =  k + 6

Subtract 6 from each side. 

6  =  k

So, the value of k is 6. 

Problem 5 :

If the slope of a line joining (0, k) and (3, -15) is -6, find the value of k. 

Solution :

Formula for slope : 

m  =  (y₂ - y₁) / (x₂ - x₁)

Substitute m = -6, (x₁, y₁) = (0, k) and (x₂, y₂) = (3, -15).  

-6  =  (-15 - k) / (3 - 0)

-6  =  (-15 - k) / 3

Multiply each side by 3. 

-18  =  -15 - k

Add 15 to each side. 

-3  =  -k

Multiply each side by -1

3  =  k

So, the value of k is 3. 

Problem 6 :

If the slope of a line joining (k, 3) and (4, 8 ) is 5/6, find the value of k. 

Solution :

Formula for slope : 

m  =  (y₂ - y₁) / (x₂ - x₁)

Substitute m = 5/6, (x₁, y₁) = (k, 3) and (x₂, y₂) = (4, 8).  

5/6  =  (8 - 3) / (4 - k)

5/6  =  5 / (4 - k)

Cross multiply. 

5(4 - k)  =  5 ⋅ 6

Simplify.

20 - 5k  =  30

Subtract 20 from each side. 

-5k  =  10

Divide each side by -5. 

k  =  -2

So, the value of k is -2. 

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