Question

How do you find the slope given `6x-7y=14`?

Answer 1

slope `=6/7`

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'.

Rearranging 6x - 7y = 14 into this form will allow us to extract m.

Subtract 6x from both sides of the equation.

`rArrcancel(6x)-7ycancel(-6x)=14-6xrArr-7y=-6x+14`

divide terms on both sides by - 7

`(cancel(-7) y)/cancel(-7)=(-6)/(-7) x+14/(-7)rArry=6/7x-2`

Thus slope `=6/7`