Question

Use the coordinates of the labeled point to find the point-slope equation of the line

Answer 1

`y + 5 = -4(x - 2)`, option b.

Explanation:

Equation of a line:

The equation of a line, in point-slope form, is given by:

`y - y_0 = m(x - x_0)`

In which m is the slope and
`(x_0,y_0)` is the point.

Point (2,-5)

This means that
`x_0 = 2, y_0 = -5`. So

`y - y_0 = m(x - x_0)`

`y - (-5) = m(x - 2)`

`y + 5 = m(x - 2)`

Finding the slope:

When we have two points, the slope is given by the change in x divided by the change in y.

In this question, we have points (0,3) and (2,-5). So

Change in y: 3 - (-5) = 3 + 5 = 8

Change in x: 0 - 2 = -2

So

`m = (8)/(-2) = -4`

Then, the equation of the line is:

`y + 5 = -4(x - 2)`, option b.