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Algebra 1

Write Linear Functions from a Graph: Mini-Lesson Review

Algebra 1Write Linear Functions from a Graph: Mini-Lesson Review
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Mini Lesson Question

Question #1: Write Linear Functions from a Graph

Which function could represent the graph?

  1. f ( x ) = − 2 x + 2
  2. f ( x ) = 2 x + 4
  3. f ( x ) = − 1 2 x + 4
  4. f ( x ) = − 2 x + 4

Write Linear Functions from a Graph

You can determine the slope and intercept of a line if the equation is written in slope-intercept form, y = m x + b y = m x + b . You can also do the reverse—identify the slope and y y -intercept and use them to find the equation of the line.

Write the linear function shown in the graph.

The graph shows the x y-coordinate plane. The x and y-axes each run from negative 6 to 6. A line intercepts the y-axis at (0, negative 4), passes through the plotted point (3, negative 2), and intercepts the x-axis at (4, 0).

To find the slope, choose two points on the graph. The y y -intercept is ( 0 , − 4 ) ( 0 , − 4 ) , and the graph passes through ( 3 , − 2 ) ( 3 , − 2 ) .

Step 1 - Find the slope by counting the rise and run.

m = r i s e r u n m = r i s e r u n

Step 2 - m = 2 3 m = 2 3

Step 3 - Find the y y -intercept.

y y -intercept ( 0 , − 4 ) ( 0 , − 4 )

Step 4 - Substitute the values into y = m x + b y = m x + b .

y = m x + b y = m x + b

Step 5 - y = 2 3 x = 4 y = 2 3 x = 4

Step 6 - Rewrite the equation using function notation.

f ( x ) = 2 3 x − 4 f ( x ) = 2 3 x − 4

Try it

Try It: Write Linear Functions from a Graph

Write the linear function shown in the graph.

The graph shows the x y-coordinate plane. The x and y-axes each run from negative 6 to 6. The point (3, negative 1) is plotted. A line intercepts the y-axis at (0, 3), and passes through the point (3, negative 1).

Check Your Understanding

Which linear function could represent the graph?

The graph shows the x y-coordinate plane. The x and y-axes each run from negative 6 to 6. A line intercepts the y-axis at (0, 1) and passes through the plotted point (5, 4).

Multiple Choice:

  1. f ( x ) = 3 5 x + 1 f ( x ) = 3 5 x + 1

  2. f ( x ) = 5 3 x + 1 f ( x ) = 5 3 x + 1

  3. f ( x ) = − 3 5 x + 1 f ( x ) = − 3 5 x + 1

  4. f ( x ) = 3 5 x − 5 3 f ( x ) = 3 5 x − 5 3

Video: Write Linear Equations from a Graph

Watch the following video to learn more about writing linear functions from a graph..

Khan Academy: Write Linear Equations

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