Chapter 4.4, Problem 44HP

To determine

To find: If the line through $\left(-2,4\right)\text{ to }\left(5,d\right)$ is parallel to the graph of line $y=3x+4$ then evaluate $\left(d\right)$ .

Answer to Problem 44HP

The value of $d=25$ .

Explanation of Solution

Given information:The line passes through the points $\left(-2,4\right)\text{ to }\left(5,d\right)$ is parallel to the graph of line $y=3x+4$ .

Concept used: If a line is parallel to another non vertical line then there slope are defined and are also equal.

Calculation: The line $y=3x+4$ has the slope $\left(m=3\right)$ . And, line passing through $\left(-2,4\right)\text{ to }\left(5,d\right)$ will have same slope. Therefore, by slope formula between two points,

  $\begin{array}{c}\left(3\right)=\frac{d-4}{5+2}\\ \text{or, }d-4=21\\ d=25\end{array}$