Question

What is the equation of the following line written in slope intercept form? (-5,-1)

Answer 1

`\large\boxed{y=-(2)/(3)x-(13)/(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)`

From the graph we have two points (-5, -1) and (-2, -3).

Look at the picture.

Calculate the slope:

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

Put it to the equation in slope-intercept form:

`y=-(2)/(3)x+b`

We can't read the y-intercept from the graph. Therefore put the coordinates of the point (-5, -1) to the equation and calculate b:

`-1=-(2)/(3)(-5)+b`

`-1=(10)/(3)+b` subtract 10/3 from both sides

`-(3)/(3)-(10)/(3)=b\to b=-(13)/(3)`

Finally:

`y=-(2)/(3)x-(13)/(3)`