Chapter 4.2, Problem 53PFA

To determine

The equation is represented by the graph.

Answer to Problem 53PFA

  $B.y-3=-2(x-2)$

Explanation of Solution

Given information: We have a graph of a line and a coordinate (2,3) on the line.

Formulas used: i) $m=\frac{y_2-y_1}{x_2-x_1}$ where m is slope and $(x_1,y_1),(x_2,y_2)$ any two points from the table.

ii) The point-slope form of line is $y-y_1=m(x-x_1),$ where m is slope and $(x_1,y_1)$ is coordinate of a point on the line.

From the graph, we can see that line crosses y -axis at 7. Therefore, coordinate of y -intercept is (0,7).

Plugging $(x_1,y_1)=\left(2,3\right)$ and $(x_2,y_2)=\left(0,7\right)$ in slope formula $m=\frac{y_2-y_1}{x_2-x_1}$ .

We get,

  $m=\frac{7-3}{0-2}=-\frac{4}{2}=-2$ .

Plugging the value of m = $-2$ and $(x_1,y_1)=(2,3)$ in $y-y_1=m(x-x_1)$ .

$y-3=-2(x-2)$

Therefore, equation in option $B.y-3=-2(x-2)$ is represented by graph.