Question

How do you find the slope and intercept of `5x + 2y = 10`?

Answer 1

slope `=-5/2`
y-intercept = 5

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 5x + 2y = 10 into this form.

subtract 5x from both sides

`cancel(5x)+2ycancel(-5x)=10-5xrArr2y=-5x+10`

now divide both sides by 2

`(cancel(2)^1 y)/cancel(2)^1=(-5)/2 x+10/2rArrcolor(red)(|bar(ul(color(white)(a/a)color(black)(y=-5/2 x+5)color(white)(a/a)|)))`

`rArr" slope" =-5/2" and y-intercept" =5`