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Algebra 1

1.12.2 Writing an Equation Given the Slope and y -intercept

Algebra 11.12.2 Writing an Equation Given the Slope and y -intercept
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Activity

Recall that the slope-intercept form of the equation of a line is y = m x + b y = m x + b , where m m is the slope and b b is the 𝑦 𝑦 -intercept. The 𝑦 𝑦 -intercept is the point where the graph crosses the 𝑦 𝑦 -axis. For 𝑦 𝑦 -intercept 𝑏 𝑏 , the coordinates of the point are ( 0 , 𝑏 ) ( 0 , 𝑏 ) .

In the following activity, you will complete a series of questions regarding this information.

Self Check

Write the equation of a line in slope-intercept form with a slope of  − 3 4 and a y -intercept of − 2 .
  1. y = 3 4 x − 2
  2. 3 x + 4 y = − 8
  3. y = − 3 4 x + 2
  4. y = − 3 4 x − 2

Additional Resources

Write Equations Given a Slope and y y -Intercept

We 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 . Now we will do the reverse—we will start with the slope and y y -intercept and use them to find the equation of the line.

Example 1

Find the equation of a line with slope − 1 − 1 and y y -intercept ( 0 , − 3 ) ( 0 , − 3 ) .

Solution

Step 1 - Name the slope.

m = − 1 m = − 1

Step 2 - Name the y y -intercept.

b = − 3 b = − 3

Step 3 - Substitute the values into y = m x + b y = m x + b .

y = − 1 x + − 3 y = − 1 x + − 3

y = − x − 3 y = − x − 3

The same information can be picked up from a graph of a line.

Example 2

Find the equation of the line shown in the graph.

A line with positive slope on a coordinate grid. A teal point is marked on the line at (3, -2), and both axes range from -8 to 8.

Solution

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

From ( 0 , − 4 ) ( 0 , − 4 ) to ( 3 , − 2 ) ( 3 , − 2 ) , the slope is m = 2 3 m = 2 3 .

Step 2 - Find the y y -intercept.

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

b = − 4 b = − 4

Step 3 - Substitute the values into y = m x + b y = m x + b .

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

y = 2 3 x − 4 y = 2 3 x − 4

Try it

Try It: Write Equations Given a Slope and y y -Intercept

Write the equation of the line graphed below in slope-intercept form:

This figure has a graph of a straight line on the x y-coordinate plane. The x and y-axes run from negative 8 to 8.

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