Question

Compare Look at these equations. Do you think they are all linear equations? Can they

all be written in the form y = mx + b? If so, show how. y=2x-3 , y-2=x+2 , 3x=9+3y

Answer 1

Yes they can all be written in y = mx + b. You just have to move the terms around.

Explanation:

y = 2x -3, this is already in slope-intercept form

Now, y - 2 = x + 2: We can add 2 on both sides to cancel out the one on the left side:

y - 2 = x + 2

y - 2 + 2 = x + + 2

y = x + 4 <-- This is in y = mx + b form

Now the last one, 3x = 9 + 3y

We can first divide all terms by 3,

3x = 9 + 3y

/3 /3 /3

x = 3 + y: Then we can subtract 3 from both sides:

x - 3 = 3 + y - 3

x - 3 = y

These are all linear equations because none of the x's have bigger powers than 1. x^2 is a quadratic equation and x^3 is cubic equation.