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Write 2y+7=3(x+5) in slope intercept form.
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Solution:

We know that:

  • Slope intercept form: y = mx + b
  • Given equation: 2y + 7 = 3(x + 5)

Simplify the distributive property.

  • 2y + 7 = 3(x + 5)
  • => 2y + 7 = 3x + 15

According to the slope intercept form formula, all the constants should be on the RHS side. Let's do the same with this equation.

Subtract 7 both sides

  • 2y + 7 - 7 = 3x + 15 - 7
  • => 2y = 3x + 8

Since 2y = 3x + 8 must be in y = mx + b form, we need to isolate the coefficient of y. To isolate the coefficient of y, divide both sides by 2.

Divide 2 both sides.

  • 2y/2 = 3x/2 + 8/2
  • y = 1.5x + 4

The slope intercept form of 2y+7=3(x+5) is y = 1.5x + 4.

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