Question

Which point-slope equation represents a line that passes through (3, –2) with a slope of -4/5?

y – 3 = –4/5 (x + 2)
y – 2 = 4/5 (x – 3)
y + 2 = –4/5 (x – 3)
y + 3 = 4/5 (x + 2)

Answer 1

The third option:

y - (-2) = -4/5(x - 3)
y + 2 = -4/5(x - 3)

Answer 2

`y+2=-(4)/(5)(x-3)`

C is correct equation.

Explanation:

We are given a point and slope of a line. Using point slope form formula to find the equation of line and match the correct option.

Formula:

`y-y_1=m(x-x_1)`

where,

`slope (m)=-(4)/(5)`

`Point:(x_1,y_1)\rightarrow (3,-2)`

Equation of line:

`y-(-2)=-(4)/(5)(x-3)`

`y+2=-(4)/(5)(x-3)`

Thus, C is correct equation of given information.