Chapter 4, Problem 5PT

To determine

To find:The equation of the line for the given condition.

Answer to Problem 5PT

The equation of the straight line is $y=3x+1$ .

Explanation of Solution

Given:

The equation passes through points $\left(1,4\right)$ and $\left(3,10\right)$

Calculation:

The standard form of line passing through two points is $y-y_1=\frac{y_2-y_1}{x_2-x_1}\left(x-x_1\right)$ .

Here $\frac{y_2-y_1}{x_2-x_1}$ is the slope of the straight line. $\left(x_1,y_1\right)$ and $\left(x_2,y_2\right)$ are the points from which the straight line passes.

Substitute $\left(1,4\right)$ for $\left(x_1,y_1\right)$ and $\left(3,10\right)$ for $\left(x_2,y_2\right)$ .

The equation of the straight line is

  $\begin{array}{l}y-y_1=\frac{y_2-y_1}{x_2-x_1}\left(x-x_1\right)\\ y-4=\frac{10-4}{3-\left(1\right)}\left(x-\left(1\right)\right)\\ y-4=\frac{6}{2}\left(x-1\right)\\ y=3x-3+4\\ y=3x+1\end{array}$

Therefore, the equation of the straight line is $y=3x+1$ .