Question

What is the equation of a line which passes through points (-5,2) and (4,-1)

Answer 1

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

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We have the points (-5, 2) and (4, -1). Substitute:

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

Put the value of the slope and the coordinates of the point (-5, 2) to the equation of a line:

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

`2=(5)/(3)+b` subtract 5/3 from both sides

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

Finally:

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