Chapter 8.4, Problem 53E

To determine

The slope of the line through the point $(0,0)$ is 2. Which point is also on the line?

Answer to Problem 53E

The point (2,4) is on the line and option G is the correct choice.

Explanation of Solution

Given:

Four choices: $\text{F}\text{. }(-4,2)\text{ G}\text{. }(2,4)\text{ H}\text{. }(-2,4)\text{ I}\text{. (2,}-\text{4)}$

Concept used:

  $\begin{array}{l}m=\frac{y_2-y_1}{x_2-x_1},\text{where,}\\ m=\text{Slope of line,}\\ y_2-y_1=\text{Difference between two }y\text{-coordinates}\\ x_2-x_1=\text{Difference between two }x\text{-coordinates of same }y-\text{coordinates}\end{array}$

Calculation:

We will check coordinates of each given point in slope formula as shown below:

  $\begin{array}{l}m=\frac{y_2-y_1}{x_2-x_1}\\ m=\frac{2-0}{-4-0}\\ m=\frac{2}{-4}\\ m=-\frac{1}{2}\end{array}$

Since slope of the point given in option F and (0,0) is not 2, therefore, option F is not a correct choice.

  $\begin{array}{l}m=\frac{y_2-y_1}{x_2-x_1}\\ m=\frac{4-0}{2-0}\\ m=\frac{4}{2}\\ m=2\end{array}$

Since slope of the point given in option G and (0,0) is 2, therefore, option Gis the correct choice.

  $\begin{array}{l}m=\frac{y_2-y_1}{x_2-x_1}\\ m=\frac{4-0}{-2-0}\\ m=\frac{4}{-2}\\ m=-2\end{array}$

Since slope of the point given in option H and (0,0) is not 2, therefore, option H is not a correct choice.

  $\begin{array}{l}m=\frac{y_2-y_1}{x_2-x_1}\\ m=\frac{-4-0}{2-0}\\ m=\frac{-4}{2}\\ m=-2\end{array}$

Since slope of the point given in option I and (0,0) is not 2, therefore, option I is not a correct choice.