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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

1.12.2 Writing an Equation Given the Slope and y -intercept

1.12.2 • Writing an Equation Given the Slope and y -intercept

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.

For questions 1 – 3, determine the slope, m m , and the y y -intercept, b b .

1.

y = 2 x + 5 y = 2 x + 5

2.

y = − 3 x + 2 y = − 3 x + 2

3.

y = − 1 5 x − 1 y = − 1 5 x − 1

For questions 4 – 7, match the correct slope and y y -intercept to the given equations.

  1. slope: − 1 2 − 1 2 , y y -intercept: − 3 − 3
  2. slope: 2 2 , y y -intercept: − 3 − 3
  3. slope: − 2 − 2 , y y -intercept: 3 3
  4. slope: 3 3 , y y -intercept: − 2 − 2
4.

What is the correct slope and y y -intercept of y = − 2 x + 3 y = − 2 x + 3 ?

5.

What is the correct slope and y y -intercept of y = 3 x − 2 y = 3 x − 2 ?

6.

What is the correct slope and y y -intercept of y = 2 x − 3 y = 2 x − 3 ?

7.

What is the correct slope and y y -intercept of y = − 1 2 x − 3 y = − 1 2 x − 3 ?

8.

Write the equation of a line, in slope-intercept form, that has a slope of −9 −9 and a y y -intercept at ( 0, −4 ) ( 0, −4 ) .

9.

Write the equation of a line, in slope-intercept form, that has a slope of 2 5 2 5 and a y y -intercept at ( 0, −4 ) ( 0, −4 ) .

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.

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

Write Equations Given a Slope and y y -Intercept

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

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