Question

Slope-intercept form of the equation for the line?

Answer 1

`\large\boxed{y=-(3)/(10)x+(1)/(2)}`

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 the points from the graph (-5, 2) and (5, -1).

Substitute:

`m=(-1-2)/(5-(-5))=(-3)/(10)=-(3)/(10)`

We have the equation in form:

`y=-(3)/(10)x+b`

Put the coordinates of the point (5, -1) to the equation:

`-1=-(3)/(10)(5)+b`

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

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

`(1)/(2)=b\to b=(1)/(2)`