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Algebra 1

Find Slope: Mini-Lesson Review

Algebra 1Find Slope: Mini-Lesson Review

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Mini Lesson Question

Question #1: Find Slope

What is the slope of the line that goes through points A and D ?

4 points on a coordinate grid, origin O.

  1. 1 2
  2. 1 2
  3. -2
  4. 2

Find the Slope of a Line Using Points on a Graph

The slope of a line is the ratio of the change in y y and the change in x x . You can use the slope formula, m = y 2 y 1 x 2 x 1 m = y 2 y 1 x 2 x 1 , to find the slope of the line through points ( x 1 , y 1 ) ( x 1 , y 1 ) and ( x 2 , y 2 ) ( x 2 , y 2 ) .

A coordinate grid with points labeled: A at (2, 3), B at (4, 0), C at (−2, 5), D at (−1, −3), and the origin O at (0, 0). The x- and y-axes are marked from −6 to 6.

Find the slope of the line that goes through points

  1. A A and D D
  2. A A and B B
  3. C C and D D

Here’s how to find the slope given two points.

a.

Step 1 - First, name B ( 3 , 4 ) B ( 3 , 4 ) as point 1 and D ( 4 , 3 ) D ( 4 , 3 ) as point 2.

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

( 3 , 4 ) ( 3 , 4 )  and  ( 4 , 3 ) ( 4 , 3 )

Step 2 - Use the slope formula.

m = y 2 y 1 x 2 x 1 m = y 2 y 1 x 2 x 1

Step 3 - Substitute the values: y 2 = 3 y 2 = 3 , y 1 = 3 y 1 = 3 , x 2 = 1 x 2 = 1 , x 1 = 2 x 1 = 2 .

m = 3 3 1 2 m = 3 3 1 2

Step 4 - Simplify.

m = 6 3 m = 6 3

m = 2 m = 2

b.

Step 1 - First, name A ( 2 , 3 ) A ( 2 , 3 ) as point 1 and B ( 4 , 1 ) B ( 4 , 1 ) as point 2.

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

( 2 , 3 ) ( 2 , 3 )  and  ( 4 , 1 ) ( 4 , 1 )

Step 2 - Use the slope formula.

m = y 2 y 1 x 2 x 1 m = y 2 y 1 x 2 x 1

Step 3 - Substitute the values: y 2 = 1 y 2 = 1 , y 1 = 3 y 1 = 3 , x 2 = 4 x 2 = 4 , x 1 = 2 x 1 = 2 .

m = 1 3 4 2 m = 1 3 4 2

Step 4 - Simplify.

m = 4 2 m = 4 2

m = 2 m = 2

c.

Step 1 - First, name C ( 2 , 5 ) C ( 2 , 5 ) as point 1 and D ( 1 , 3 ) D ( 1 , 3 ) as point 2.

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

( 2 , 5 ) ( 2 , 5 )  and  ( 1 , 3 ) ( 1 , 3 )

Step 2 - Use the slope formula.

m = y 2 y 1 x 2 x 1 m = y 2 y 1 x 2 x 1

Step 3 - Substitute the values: y 2 = 3 y 2 = 3 , y 1 = 5 y 1 = 5 , x 2 = 1 x 2 = 1 , x 1 = 2 x 1 = 2 .

m = 3 5 1 ( 2 ) m = 3 5 1 ( 2 )

Step 4 - Simplify.

m = 8 1 m = 8 1

m = 8 m = 8

Try it

Try It: Find the Slope of a Line Using Points on a Graph

Find the slope of the line that goes through points B B and D D .

A coordinate grid with points labeled: A at (2, 3), B at (4, 0), C at (−2, 5), D at (−1, −3), and the origin O at (0, 0). The x- and y-axes are marked from −6 to 6.

Check Your Understanding

What is the slope of the line that goes through points A A and D D ?

A coordinate grid with points labeled: A at (2, 3), B at (4, 0), C at (−2, 5), D at (−1, −3), and the origin O at (0, 0). The x- and y-axes are marked from −6 to 6.

Multiple Choice:

  1. 1 4 1 4

  2. 1 4 1 4

  3. 3 3

  4. 3 3

Videos: Finding the Slope of a Line

Khan Academy: Slope from a Graph

Watch this video to see how to find the slope from a graph.

Khan Academy: Slope from Two Points

Watch this video to see how to find the slope given two points.

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