Linear Equations Standard to Slope Intercept Form

Converting Equations from Standard form to Slope-Intercept form.

Equation in Slope Intercept Form

Standard form of a linear equation.

Open Ended

Based on what you have learned about linear equations written in slope-intercept form, what do you notice as the difference between slope-intercept form and standard form?

How can we convert the equation from standard form to slope intercept form?

• First, add or subtract the "x" term to move it to the other side using opposite operations.

• ​Next, divide by the coefficient away from the "y". This isolates the "y" variable.

• ​Lastly, simplify if possible.

• The equations will now be written in slope-intercept form!

​What is looks like in action!

Let's Practice: Convert the equation into slope-intercept form: 3x - 3y = 9

• Subtract 3x from each side.

  • 3x - 3x = 0, so we are left with -3y = -3x + 9

• Divide the -3 on each side to isolate the "y": 3y/3 = y

  • y = -3x/-3 + 9/-3

    • y = x -3

• Now graph it graph it!

• https://www.desmos.com/calculator

• Subtract 3x from each side.

  • 3x - 3x = 0, so we are left with: -3y = -3x + 9

• Divide the -3 on each side to isolate the "y": 3y/3 = y

  • y = -3x/-3 + 9/-3

    • y = x -3

  • Now graph it graph it!

  • https://www.desmos.com/calculator

Multiple Choice

Convert the following equation from standard form to slope-intercept form: 5x - 5y = 25

• y = x - 5
• y = 5x - 1
• y = -x + 5
• y = 5x + 1

Multiple Choice

Convert the following equation from standard form to slope-intercept form: 4x + 2y = 14

• y = 4x + 14

• y = -2x + 14

• y = -2x - 14

• y = -2x + 7

Multiple Choice

Convert the following equation from standard form to slope-intercept form: -9x +3y = -12

• y = -3x - 4

• y = -3x + 4

• y = 3x + 4

• y = 3x - 4