Compare the two sets of equations below. One set is presented in slope-intercept form, and the other set is not.

How can you tell if an equation is written in slope-intercept form?

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Slope-intercept form of a linear equation is y = mx + b. If an equation is written in slope-intercept form, you can tell because it has “y =” by itself with no other constants or terms.

One way to determine the slope of a line, given its equation, is to change the equation to slope-intercept form, and then identify the coefficient of the x term. The coefficient of the x term is the slope of the line.

To write an equation in slope-intercept form, you must solve the equation for y.

Directions:

1. Copy the table below into your notes.
2. Solve the equation for y, determine the slope, and then write your solutions in the table.
3. Use the Equation Calculator and Solver below to check your answers. Click on the image to access the Equation Calculator and Solver.
4. After you use the Equation Calculator and Solver, click on the link below to see a completed table.

Equation Calculator and Solver

Need help using the Equation Solver? Click to see an image with Interactive popup. Assistance may be required.additional directions. Interactive popup. Assistance may be required.

Check Your Answer

Equation	Equation in Slope-Intercept Form	Slope
-5x + y = 10	y = 5x + 10	5
3y + 15x = 8	y = -5x + eight-thirds 8 3	-5
-4 + 2y = 10	y = 7	0
-y = two-thirds 2 3 x	y = - two-thirds 2 3 x	- two-thirds 2 3
6y + 3x = 18	y = - one-half 1 2 x + 3	- one-half 1 2

Pause and Reflect

List the slopes from your table in order from least to greatest.

Need a hint?

Use a number line to plot the numbers representing the slopes. The number that is farthest to the left is the least number.

Check Your Answer

-5, -2 over 3 - 2 3 , 1 over 2 - 1 2 , 0, 5

Which of the slopes are greater than −1?

Need a hint?

Use a number line to plot the numbers representing the slopes. The numbers to the right of −1 are greater than −1.

Check Your Answer

-2 over 3 - 2 3 , -1 over 2 - 1 2 , 0 , and 5

Practice

Determine the slopes of the lines represented by each of the equations below.

1. y = 0.45x – 18

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   Need a hint?

   Is the equation written in slope-intercept form (i.e., solved for y)? If so, the slope is the coefficient of x. If not, solve the equation for y, and then determine the coefficient of x.
   Interactive popup. Assistance may be required.

   Check Your Answer

   Slope = 0.45


2. y = 15 6 x – 18

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   Need a hint?

   Is the equation written in slope-intercept form (i.e., solved for y)? If so, the slope is the coefficient of x. If not, solve the equation for y, and then determine the coefficient of x.
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   Check Your Answer

   Slope = 15 6


3. 5x + 8y = 38

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   Need a hint?

   Is the equation written in slope-intercept form (i.e., solved for y)? If so, the slope is the coefficient of x. If not, solve the equation for y, and then determine the coefficient of x.
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   Check Your Answer

   


4. 3.2x + 1.6y = 72

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   Need a hint?

   Is the equation written in slope-intercept form (i.e., solved for y)? If so, the slope is the coefficient of x. If not, solve the equation for y, and then determine the coefficient of x.
   Interactive popup. Assistance may be required.

   Check Your Answer