Question

How do you write an equation of a line given (7,-4) and m=2/5?

Answer 1

See below.

Explanation:

This is an example of the use for point-slope form for a line.

Point-slope form shows the relationship between the slope of a line and a point on the line, or mathematically, `y-y_0=m(x-x_0)`, where `(x_0, y_0)` is the point, and `m` is the slope.

Given that `(x_0, y_0)=(7,-4)`, and `m=frac(2)(5)`, we plug these into the equation.

`y-(-4)=frac(2)(5)(x-7)`
`y=frac(2)(5)(x)-frac(14)(5)-4`

`y=frac(2)(5)(x)-frac(34)(5)`