Question

How do you find the slope and intercept of `4x + 7y = 28`?

Answer 1

slope `=-4/7`
y-intercept = 4

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 is the slope and b, the y-intercept.

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

now rearrange 4x + 7y = 28 into this form.

hence : 7y = -4x+28

divide both sides by 7

`(cancel(7) y)/cancel(7)=(-4)/7 x+(cancel(28)^4)/cancel(7)^1`

`rArry=-4/7x+4" is the equation"`

thus slope `=-4/7" and y-intercept"=4`