Question

Write the equation of the line in slope-intercept form that has the following points: (2, -1)(5, -3)

Answer 1

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

Explanation:

The skope-intercept form:

`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 (2, -1) and (5, -3). Substitute:

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

We have the equation:

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

Put the coordinates of the point (2 , -1) to the equation:

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

`-1=-(4)/(3)+b` add 4/3 to both sides

`(1)/(3)=b\to b=(1)/(3)`

Finally we have:

`y=-(2)/(3)x+(1)/(3)`