Question

What is the slope and y-intercept of this line 8x + 6y = 12?

Answer 1

slope`=-4/3`
y-intercept = 2

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 equation in this form is useful as m and b can be extracted 'easily'

If we rearrange 8x + 6y = 12 into this form then m and b can be found.

hence : 6y = 12 - 8x = - 8x +12

divide both sides by 6.

`rArr(cancel(6) y)/cancel(6)=(-8)/6 x+12/6" and simplifying gives"`

`y=-4/3x+2`

`rArr"slope"=-4/3" and y-intercept"=2`