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