Question

Find an equation for these points (-5,5) (4,2)

Answer 1

`\large\boxed{y=-(1)/(3)x+(10)/(3)}`

Explanation:

The slope-intercept form of an equation of a line:

`y=mx+b`

m - slope

b - y-intercept

The formula of a slope:

`m=(y_2-y_1)/(x_2-x_1)`

We have two points (-5, 5) and (4, 2).

substitute:

`m=(2-5)/(4-(-5))=(-3)/(9)=-(1)/(3)`

Put the value os a slope and coordinates of the point (4, 2) to the equation of a line:

`2=-(1)/(3)(4)+b`

`2=-(4)/(3)+b` add 4/3 to both sides

`2(4)/(3)=b\to b=3(1)/(3)\to b=(10)/(3)`