Chapter 8.8, Problem 11CYU

To determine

To calculate:To write equation of a line that passes through $\left(-1,-6\right)$ , $\left(0,-2\right)$ , $\left(1,2\right)$ and $\left(2,6\right)$ .

Answer to Problem 11CYU

The equation of the line that passes through $\left(-1,-6\right)$ , $\left(0,-2\right)$ , $\left(1,2\right)$ and $\left(2,6\right)$ is $y=4x-2$

Explanation of Solution

Given information:

Points - $\left(-1,-6\right)$ , $\left(0,-2\right)$ , $\left(1,2\right)$ and $\left(2,6\right)$

Formula Used:

The slope-intercept form of the equation of a line is $y=mx+b$ , where $m$ is the slope of the line, and $b$ is the y-intercept.

In case of two points given $\left(x_1,y_1\right)$ and $\left(x_2,y_2\right)$ , slope is given by

  $m=\frac{y_2-y_1}{x_2-x_1}$

Calculation:

GivenPoints - $\left(-1,-6\right)$ , $\left(0,-2\right)$ , $\left(1,2\right)$ and $\left(2,6\right)$

Using the above explanation, we have slope of the line as −

  $m=\frac{y_2-y_1}{x_2-x_1}$

Substituting the two values, we have:

  $m=\frac{-2+6}{0+1}$

Solving the above equation, we have:

  $m=4$

Using the above explanation, we have equation of the line as −

  $y=mx+b$

Substituting the value of one of the points $\left(1,2\right)$ and slopein the above equation, we have:

  $2=\left(1\right)\left(4\right)+b$

Solving the above equation, we have :

  $b=-2$

Thus, the equation of the line is

  $y=4x+\left(-2\right)$

Solving further, we have :

  $y=4x-2$

Thus, the equation of the line is $y=4x-2$