Question

What is the slope of the line `6x - 3y = - 54` ?

Answer 1

slope = 2

Explanation:

The equation of a line in 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 benefit of having the line in this form is that the slope and y-intercept can be extracted 'easily'.

Rearrange 6x - 3y = - 54 into this form.

hence : - 3y = -6x - 54

divide both sides by -3

`rArr(cancel(-3)^1 y)/cancel(-3)^1=(cancel(-6)^2x)/cancel(-3^1)+cancel(-54)^(18)/cancel(-3)^1`

Thus : y = 2x + 18

`rArr"slope"=2`