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Convert the following linear equations into the form y = mx + c: a) 2y = 4x + 8 b) x − y = 5 d) 3x + 4y + 3 = 0

Mathematics

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Answers

3 parts
a

y=2x+4y = 2x + 4

b

y=x−5y = x - 5

d

y=−34x−34y = -\frac{3}{4}x - \frac{3}{4}

Step-by-step solution

5 steps

Here are the solutions for the equations in the form y=mx+cy = mx + c:

Part a· 1 step

2y=4x+82y = 4x + 8

  1. Divide both sides of the equation by 2.

    2y2=4x2+82\frac{2y}{2} = \frac{4x}{2} + \frac{8}{2} y=2x+4y = 2x + 4

    The equation in the form y=mx+cy = mx + c is y=2x+4\boxed{y = 2x + 4}.

Part b

y=x−5y = x - 5

x−y=5x - y = 5

  1. Subtract xx from both sides of the equation.

    −y=5−x-y = 5 - x

  2. Multiply the entire equation by −1-1 to solve for yy.

    y=−5+xy = -5 + x y=x−5y = x - 5

    The equation in the form y=mx+cy = mx + c is y=x−5\boxed{y = x - 5}.

Part d

y=−34x−34y = -\frac{3}{4}x - \frac{3}{4}

3x+4y+3=03x + 4y + 3 = 0

  1. Subtract $3x$ and 3 from both sides of the equation.

    4y=−3x−34y = -3x - 3

  2. Divide the entire equation by 4 to isolate yy.

    4y4=−3x4−34\frac{4y}{4} = \frac{-3x}{4} - \frac{3}{4} y=−34x−34y = -\frac{3}{4}x - \frac{3}{4}

    The equation in the form y=mx+cy = mx + c is y=−34x−34\boxed{y = -\frac{3}{4}x - \frac{3}{4}}.

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