Chapter 3.2, Problem 2AYU

Find an equation of the line containing the points $\left(1,4\right)$ and $\left(3,8\right)$. (pp. 35-36)

To determine

To calculate: An equation of the line containing the given points.

Answer to Problem 2AYU

Solution:

The equation of the line passing through the given points is $y=2x+2$.

Explanation of Solution

Given:

The given points are $(1,4)$ and $(3,8)$.

Formula used:

The point-slope form of the equation of a line passing through 2 points $(x_1,y_1)$ and $(x_2, y_2)$ is

$y-y_1=\left(\frac{y_2-y_1}{x{}_2-x{}_1}\right)(x-x_1)$

Calculation:

Here, we have $(x_1,y_1)=(1,4)$ and $(x_2,y_2)=(3,8)$.

Therefore, the equation of the line is

$y-4=\left(\frac{8-4}{3-1}\right)(x-1)$

$\Rightarrow y-4=2x-2$

$\Rightarrow y=2x-2+4$

$\Rightarrow y=2x+2$

Thus, the equation of the given line is $y=2x+2$.