Question

What equation is graphed in this figure? y+2=−32(x−2) y−3=32(x+1) y+1=−23(x−3) y−4=−23(x+2) Number graph that ranges from negative five to five on the x and y axes. A line passes through begin ordered point zero comma one end ordered pair and begin ordered pair two comma negative two end ordered pair

Answer 1

Answer:

$y+2=-\frac{3}{2}(x-2)$

Step-by-step explanation:

Given:

Two points on a line are given as:

(0, 1)  and (2, -2)

We know that the slope of a line passing through points $(x_1,y_1)\ and\ (x_2,y_2)$ is given as:

$m=\frac{y_2-y_1}{x_2-x_1}$

Plug in $x_1=0,y_1=1,x_2=2,y_2=-2$. This gives,

$m=\frac{-2-1}{2-0}\\\\m=\frac{-3}{2}=-\frac{3}{2}$

The equation of a line with slope 'm' and points $(x_1,y_1)\ and\ (x_2,y_2)$ is given as:

$y-y_1=m(x-x_1)\\\\or\\\\y-y_2=m(x-x_2)$

Now, on plugging in the second point $(x_2,y_2)=(2,-2)$ we get:

$y-(-2)=-\frac{3}{2}(x-2)\\\\y+2=-\frac{3}{2}(x-2)$

Therefore, the first option is correct which is given as:

$y+2=-\frac{3}{2}(x-2)$