Question

Write each equation in slope-intercept form. (-1/2)x+y =4 2x-3y=8

Answer 1

Recall that the slope intercept of a line equation is

y = mx+b

where m is the slope and b is the y-intercept. Given the line equations, we should operate both sides of it, so we end up having the y term on one side on its own.

First, we start with the equation

`\text{ -}(1)/(2)x+y=4`

By adding (1/2)x on both sides, we get

`y=(1)/(2)x+4`

which is the slope-intercept form of this line equation.

On the other side, we have the equation

`2x\text{ -3y=8}`

First, we start by adding 3y on both sides, so we get

`2x\text{ = 8+3y}`

Then, we subtract 8 on both sides, so we have

`3y\text{ = 2x-8}`

Finally, we divide both sides by 3, so we get

`y=\frac{2x\text{ -8}}{3}=(2)/(3)x\text{ -}(8)/(3)`

which is the slope intercept form of the second line equation.