THE SLOPE FORMULA WORKSHEET

Problem 1 : 

Find the slope of the line that contains (5, -3) and (-2, 3).

Problem 2 : 

Find the slope of the line that contains (-2, -2) and (7, -2).

Problem 3 : 

A line passes through the points (3/4, 7/5) and (1/4, 2/5). Find its slope. 

Problem 4 : 

Problem 5 :

Problem 6 : 

Problem 7 : 

Problem 8 : 

Find the slope of the line described by 6x - 5y = 30.

Problem 9 : 

Find the slope of the line described by 2x + 3y = 12.

Problem 10 : 

The graph shows how much water is in a reservoir at different times. Find the slope of the line. Explain what the slope represents.

Detailed Answer Key

1. Answer :

Use the slope formula.

m  =  (y₂ - y₁)/(x₂ - x₁)

Substitute (4, -2) for (x₁ , y₁) and (-1, 2) for (x₂,  y₂).

m  =  [3 - (-3)]/(-2 - 5)

m  =  (3 + 3)/(-7)

m  =  6/(-7)

m  =  -6/7

The slope of the line that contains (5, -3) and (-2, 3) is -6/7.

2. Answer :

Use the slope formula.

m  =  (y₂ - y₁)/(x₂ - x₁)

Substitute (-2, -2) for (x₁ , y₁) and (7, -2) for (x₂,  y₂).

m  =  [-2 - (-2)]/[7 - (-2)]

m  =  (-2 + 2)/(7 + 2)

m  =  0/9

m  =  0

The slope of the line that contains (-2, -2) and (7, -2) is 0.

3. Answer :

Use the slope formula.

m  =  (y₂ - y₁)/(x₂ - x₁)

Here, 

(x₁ , y₁)  =  (3/4, 7/5)  

(x₂,  y₂)  =  (1/4, 2/5)

Then, 

m  =  (2/5 - 7/5)/(1/4 - 3/4)

m  =  (-5/5) / (-2/4)

m  =  (-1) / (-1/2)

m  =  (-1)(-2/1)

m  =  2

The slope of the line that contains (-2, -2) and (7, -2) is 0.

4. Answer :

Let (-2, -1) be (x₁, y₁) and (2, 2) be (x₂ , y₂).

Use the slope formula.

m  =  (y₂ - y₁)/(x₂ - x₁)

Substitute (-2, -1) for (x₁ , y₁) and (2, 2) for (x₂,  y₂).

m  =  [2 - (-1)]/[2 - (-2)]

m  =  (2 + 1)/(2 + 2)

m  =  3/4

The slope of the line is 3/4.

5. Answer :

Let (-2, 4) be (x₁, y₁) and (0, -2) be (x₂ , y₂).

Use the slope formula.

m  =  (y₂ - y₁)/(x₂ - x₁)

Substitute (-2, 4) for (x₁ , y₁) and (0, -2) for (x₂,  y₂).

m  =  (-2 - 4)/[0 - (-2)]

m  =  -6/(0 + 2)

m  =  -6/2

m  =  -3

The slope of the line is -3.

6. Answer :

Choose any two points from the table.

Let (2, 0) be (x₁, y₁) and (2, 3) be (x₂ , y₂).

Use the slope formula.

m  =  (y₂ - y₁)/(x₂ - x₁)

Substitute (2, 0) for (x₁ , y₁) and (2, 3) for (x₂,  y₂).

m  =  (3 - 0)/(2 - 2)

m  =  3/0

m  =  Undefined

The slope is undefined.

7. Answer :

Choose any two points from the table.

Let (0, 1) be (x₁, y₁) and (5, 11) be (x₂ , y₂).

Use the slope formula.

m  =  (y₂ - y₁)/(x₂ - x₁)

Substitute (0, 1) for (x₁ , y₁) and (5, 11) for (x₂,  y₂).

m  =  (11 - 1)/(5 - 0)

m  =  10/5

m  =  2

The slope is 2.

8. Answer :

The line contains (5, 0) and (0, -6). Use the slope formula.

Use the slope formula.

m  =  (y₂ - y₁)/(x₂ - x₁)

Substitute (5, 0) for (x₁ , y₁) and (0, -6) for (x₂,  y₂).

m  =  (-6 - 0)/(0 - 5)

m  =  -6/(-5)

m  =  6/5

The slope is 6/5.

9. Answer : 

The line contains (6, 0) and (0, 4). Use the slope formula.

Use the slope formula.

m  =  (y₂ - y₁)/(x₂ - x₁)

Substitute (6, 0) for (x₁ , y₁) and (0, 4) for (x₂,  y₂).

m  =  (4 - 0)/(0 - 6)

m  =  4/(-6)

m  =  -4/6

m  =  -2/3

The slope is -2/3.

10. Answer :

Use the slope formula.

m  =  (y₂ - y₁)/(x₂ - x₁)

Here, 

(x₁ , y₁)  =  (20, 3000)

(x₂,  y₂)  =  (60, 2000)

Then, 

m  =  (2000 - 3000)/(60 - 20)

m  =  -1000/40

m  =  -25

The slope is -25.

In the given situation, y represents volume of water and x represents time.

So slope represents

change in volume/change in time

in units of

thousands of cubic feet/hours.

A slope of -25 means the amount of water in the reservoir is decreasing (negative change) at a rate of 25 thousand cubic feet each hour.

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