Rewrite each of the following equations in y = mx + b form.

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Rewrite each of the following equations in y = mx + b form. Show each step! 1) x + y = -15 2) 2y + 8x = 1 3) -2x + y = 1 4) 3y – 2x = 9 5) 2y = -1x – 8 6) y – 4 = -3(x – 3) 2014-2015

The Correct Answer and Explanation is:

1) x+y=−15x + y = -15x+y=−15

  • Start by isolating yyy. To do this, subtract xxx from both sides of the equation. x+y−x=−15−xx + y – x = -15 – xx+y−x=−15−x y=−x−15y = -x – 15y=−x−15

This is now in y=mx+by = mx + by=mx+b form with m=−1m = -1m=−1 and b=−15b = -15b=−15.

2) 2y+8x=12y + 8x = 12y+8x=1

  • First, subtract 8x8x8x from both sides. 2y=−8x+12y = -8x + 12y=−8x+1
  • Now, divide the entire equation by 2 to solve for yyy. 2y2=−8×2+12\frac{2y}{2} = \frac{-8x}{2} + \frac{1}{2}22y​=2−8x​+21​ y=−4x+12y = -4x + \frac{1}{2}y=−4x+21​

Now it’s in the form y=mx+by = mx + by=mx+b, where m=−4m = -4m=−4 and b=12b = \frac{1}{2}b=21​.

3) −2x+y=1-2x + y = 1−2x+y=1

  • Start by isolating yyy. Add 2x2x2x to both sides. y=2x+1y = 2x + 1y=2x+1

This is in the form y=mx+by = mx + by=mx+b with m=2m = 2m=2 and b=1b = 1b=1.

4) 3y−2x=93y – 2x = 93y−2x=9

  • Add 2x2x2x to both sides to get the yyy-terms isolated. 3y=2x+93y = 2x + 93y=2x+9
  • Now, divide by 3 to solve for yyy. y=2×3+3y = \frac{2x}{3} + 3y=32x​+3

In the form y=mx+by = mx + by=mx+b, m=23m = \frac{2}{3}m=32​ and b=3b = 3b=3.

5) 2y=−x−82y = -x – 82y=−x−8

  • Divide both sides of the equation by 2 to solve for yyy. y=−x2−4y = \frac{-x}{2} – 4y=2−x​−4

So the equation is y=−12x−4y = -\frac{1}{2}x – 4y=−21​x−4, with m=−12m = -\frac{1}{2}m=−21​ and b=−4b = -4b=−4.

6) y−4=−3(x−3)y – 4 = -3(x – 3)y−4=−3(x−3)

  • First, distribute the −3-3−3 on the right-hand side. y−4=−3x+9y – 4 = -3x + 9y−4=−3x+9
  • Now, add 4 to both sides to isolate yyy. y=−3x+9+4y = -3x + 9 + 4y=−3x+9+4 y=−3x+13y = -3x + 13y=−3x+13

Now it’s in the form y=mx+by = mx + by=mx+b, with m=−3m = -3m=−3 and b=13b = 13b=13.

Final Summary:

  1. y=−x−15y = -x – 15y=−x−15
  2. y=−4x+12y = -4x + \frac{1}{2}y=−4x+21​
  3. y=2x+1y = 2x + 1y=2x+1
  4. y=2×3+3y = \frac{2x}{3} + 3y=32x​+3
  5. y=−12x−4y = -\frac{1}{2}x – 4y=−21​x−4
  6. y=−3x+13y = -3x + 13y=−3x+13

These are all in slope-intercept form, and you can easily identify the slope and y-intercept in each case.

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