Answer:
Option B is correct.
[tex]y-4=-\frac{3}{2}(x+2)[/tex]
Step-by-step explanation:
Point slope form:
The equation of straight line is given by:
[tex]y-y_1=m(x-x_1)[/tex] ......[1] where m is the slope and a point [tex](x_1, y_1)[/tex] lies on the coordinate plane
From the given graph:
Consider two points i.e,
(-2, 4) and (2, -2)
Calculate slope:
Slope(m) is given by;
[tex]m = \frac{y_2-y_1}{x_2-x_1}[/tex]
Substitute the given points we have;
[tex]m = \frac{-2-4}{2-(-2)} = -\frac{6}{4} = -\frac{3}{2}[/tex]
Now, substitute the value of m and (-2, 4) in [1] we have;
[tex]y-4=-\frac{3}{2}(x-(-2))[/tex]
or
[tex]y-4=-\frac{3}{2}(x+2)[/tex]
Therefore, the equation is graphed here is [tex]y-4=-\frac{3}{2}(x+2)[/tex]
