Standard Form to Slope-Intercept Form

Review One-Step Equations x – 7 = 12 5n = 35 x = 19 n = 7 = 3 20 + h = 41 h = 21 c = 24 We can simply work the operation backwards in our head to get the answer.

Multi-step equations When and equation has more than one operation you still have to isolate the variable by doing the following: Make sure variable terms are all on one side, and constant terms are on the other. Simplify Divide by the coefficient of the variable.

How would we solve 3x + 5 = 12? 3x + 6 = 12 1. Subtract 6 from both sides 3x = 6 2. Divide by 3 x=3

Let’s try some more equations Remember, we have to keep the equations balanced! Solve: 8m – 10 = 36 8m – 10 + 10 = 36 + 10 8m = 46 8 8 m = w = 84

Standard Form: Ax + By = C Slope Intercept Form: y = mx + b Linear Equations Standard Form: Ax + By = C Slope Intercept Form: y = mx + b

Standard Form to Slope-Intercept We can put an equation that is in standard form into y-intercept form by using our knowledge from 2-step equations! **Get the y-variable by itself** (Solve for y)

Standard Form to Slope-Intercept Isolate the y-variable: Add or Subtract the x term. Divide all terms by the coefficient of y.

Example 1 Put the equation 2x + y = 4 in slope-intercept form. 1. Subtract 2x to both sides. 2x + y = 4 -2x -2x y = 4 – 2x y is by itself! You are done **Write as y = -2x + 4

Example 2 Put the equation 8x + 4y = 12 in slope-intercept form. Subtract 8x from both sides 8x + 4y = 12 -8x -8x 4y = 12 – 8x 2. Divide by 4 to ALL TERMS 4y = 12 - 8x 4 4 4 y = 3 – 2x write as y = -2x + 3

Example 3 -5 Write as y = -x/5 - 6 Put the equation –x – 5y = 30 in slope-intercept form. Add the x to both sides –x – 5y = 30 +x +x -5y = 30 + x 2. Divide by -5 to ALL TERMS -5 y = -6 + x -5 Write as y = -x/5 - 6