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Algebra 1

4.7.2 Finding Slope From Tables, Graphs, and Points

Algebra 14.7.2 Finding Slope From Tables, Graphs, and Points

4.7.2 Finding Slope From Tables, Graphs, and Points

4.7.2 • Finding Slope From Tables, Graphs, and Points

Activity

Recall that the slope of a line is the rate of change of the linear function. On the graph, it is the steepness of the line.

1. Find the slope of the line that connects ( 0 , 0 ) ( 0 , 0 ) and ( 3 , 2 ) ( 3 , 2 )

2. Find the slope of the line that connects ( 4 , 2 ) ( 4 , 2 ) and ( 10 , 7 ) ( 10 , 7 )

3. Find the slope of the line that connects ( 1 , − 2 ) ( 1 , − 2 ) and ( 2 , 5 ) ( 2 , 5 )

4. Find the slope of the line that connects ( − 3 , 4 ) ( − 3 , 4 ) and ( − 5 , − 2 ) ( − 5 , − 2 )

5. Find the slope of the line that connects ( 8 , 3 ) ( 8 , 3 ) and ( 10 , − 9 ) ( 10 , − 9 )

For questions 6 – 9, use the graph to find the slope of the line that goes through the two points.

6. A and B

7. A and D

8. B and C

9. C and D

10. Determine the slope of the equation whose values are in the given table.

11. Determine the slope of the equation whose values are in the given table. Simplify your answer.

Self Check

Find the slope of the line that goes through ( − 1 , 5 ) and ( 6 , 2 ) .
  1. − 3 7
  2. 3 7
  3. − 7 3
  4. − 3 5

Additional Resources

Slope of a Line

Here’s how to find the slope of a line from its graph using m = r i s e r u n m = r i s e r u n .

Finding Slope from a Graph

Step 1 - Locate two points on the line whose coordinates are integers.

Step 2 - Starting with one point, sketch a right triangle, going from the first point to the second point.

Step 3 - Count the rise and the run on the legs of the triangle.

Step 4 - Take the ratio of rise to run to find the slope: m = r i s e r u n m = r i s e r u n .

Example 1

Step 1 - Locate two points on the line whose coordinates are integers. ( 0 , 5 ) ( 0 , 5 ) and ( 3 , 3 ) ( 3 , 3 )

Step 2 - Starting with one point, sketch a right triangle, going from the first point to the second point.

Step 3 - Count the rise and the run on the legs of the triangle.

The rise is -2.

The run is 3.

Step 4 - Take the ratio of rise to run to find the slope: m = r i s e r u n m = r i s e r u n .

m = − 2 3 m = − 2 3

Here’s how to find the slope of a line when given two points on the line.

Finding Slope from Two Points

Step 1 - Label the points ( x 1 , y 1 ) x 1 , y 1 ) and ( x 2 , y 2 ) x 2 , y 2 ) .

Step 2 - Substitute the values into the slope formula: m = y 2 − y 1 x 2 − x 1 m = y 2 − y 1 x 2 − x 1

Step 3 - Simplify the slope expression.

Example 2

Use the slope formula to find the slope of the line through the points ( − 2 , − 3 ) ( − 2 , − 3 ) and ( − 7 , 4 ) ( − 7 , 4 ) .

Step 1 - Label the points ( x 1 , y 1 ) ( x 1 , y 1 ) and ( x 2 , y 2 ) ( x 2 , y 2 ) .

( − 2 , − 3 ) ( − 2 , − 3 ) ( − 7 , 4 ) ( − 7 , 4 )

( x 1 , y 1 ) ( x 1 , y 1 ) ( x 2 , y 2 ) ( x 2 , y 2 )

Step 2 - Substitute into the slope formula.

m = y 2 − y 1 x 2 − x 1 = 4 − ( − 3 ) − 7 − ( − 2 ) m = y 2 − y 1 x 2 − x 1 = 4 − ( − 3 ) − 7 − ( − 2 )

Step 3 - Simplify

m = 4 − ( − 3 ) − 7 − ( − 2 ) = 4 + 3 − 7 + 2 = 7 − 5 m = 4 − ( − 3 ) − 7 − ( − 2 ) = 4 + 3 − 7 + 2 = 7 − 5

You Try: Finding Slope from a Graph or Two Points

Find the slope of the line using the graph, then confirm your answer using the slope formula.

Step 1 - Locate two points on the line whose coordinates are integers.

( 0 , 1 ) ( 0 , 1 ) and ( 5 , − 2 ) ( 5 , − 2 )

Step 2 - Starting with one point, sketch a right triangle, going from the first point to the second point.

Step 3 - Count the rise and the run on the legs of the triangle.

The rise is 3.

The run is -5.

Step 4 - Take the ratio of rise to run to find the slope: m = r i s e r u n m = r i s e r u n .

m = − 3 5 m = − 3 5

Now, using the slope formula:

Step 1 - Label the points ( x 1 , y 1 ) ( x 1 , y 1 ) and ( x 2 , y 2 ) ( x 2 , y 2 ) .

( 0 , 1 ) ( 0 , 1 ) ( 5 , − 2 ) ( 5 , − 2 )

( x 1 , y 1 ) ( x 1 , y 1 ) ( x 2 , y 2 ) ( x 2 , y 2 )

Step 2 - Substitute into the slope formula.

m = y 2 − y 1 x 2 − x 1 = − 2 − 1 5 − 0 m = y 2 − y 1 x 2 − x 1 = − 2 − 1 5 − 0

Step 3 - Simplify.

m = − 2 − 1 5 − 0 = − 3 5 m = − 2 − 1 5 − 0 = − 3 5

The slope of the line is − 3 5 − 3 5 .

Here’s how to find the slope of a line, given a table of values.

Example 3

Find the slope of the line whose table of values is shown:

Step 1 - Locate two points on the line whose coordinates are integers.

( 3 , 4 ) ( 3 , 4 ) ( 5 , 7 ) ( 5 , 7 )

Step 2 - Label the points ( x 1 , y 1 ) ( x 1 , y 1 ) and ( x 2 , y 2 ) ( x 2 , y 2 ) .

( 3 , 4 ) ( 3 , 4 ) ( 5 , 7 ) ( 5 , 7 )

( x 1 , y 1 ) ( x 1 , y 1 ) ( x 2 , y 2 ) ( x 2 , y 2 )

Step 3 - Substitute into the slope formula.

m = y 2 − y 1 x 2 − x 1 = 7 − 4 5 − 3 m = y 2 − y 1 x 2 − x 1 = 7 − 4 5 − 3

Step 4 - Simplify.

m = 7 − 4 5 − 3 = 3 2 m = 7 − 4 5 − 3 = 3 2

Try it

Finding Slope from a Table

Find the slope of the line whose table of values is shown:

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