Answer:
[tex]y + 5 = -4(x - 2)[/tex], option b.
Step-by-step explanation:
Equation of a line:
The equation of a line, in point-slope form, is given by:
[tex]y - y_0 = m(x - x_0)[/tex]
In which m is the slope and [tex](x_0,y_0)[/tex] is the point.
Point (2,-5)
This means that [tex]x_0 = 2, y_0 = -5[/tex]. So
[tex]y - y_0 = m(x - x_0)[/tex]
[tex]y - (-5) = m(x - 2)[/tex]
[tex]y + 5 = m(x - 2)[/tex]
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
[tex]m = \frac{8}{-2} = -4[/tex]
Then, the equation of the line is:
[tex]y + 5 = -4(x - 2)[/tex], option b.
