Question

How do you find the slope and intercept of `5 - 1/3y = 2x`?

Answer 1

slope = - 6 , y-intercept = +15

Explanation:

The equation of a line in `color(blue)"slope-intercept form"` is

`color(red)(|bar(ul(color(white)(a/a)color(black)(y=mx+b)color(white)(a/a)|)))`
where m represents the slope and b, the y-intercept.

The advantage to having the equation in this form is that m and b , may be extracted 'easily'.

Rearrange `5-1/3y=2x" in this form"`

subtract 5 from both sides.

`rArrcancel(5)-cancel(5)-1/3y=2x-5rArr-1/3y=2x-5`

multiply through by - 1 : `1/3y=-2x+5`

now multiply both sides by 3.

`rArrcancel(3)^1xx1/cancel(3)^1 y=-6x+15rArry=-6x+15`

The equation is now in the form `color(blue)(y=mx+b)`

`rArr"slope" =-6" and y-intercept" =+15`
graph{-6x+15 [-45.63, 45.6, -22.74, 22.9]}