Chapter 8.5, Problem 6OE

To determine

To find: The equation in slope intercept form of the given line.

Answer to Problem 6OE

The equation in slope intercept form of the given line is $y=x+1$ .

Explanation of Solution

Given information:

The points through the line passes is $\left(1,4\right),\left(2,5\right)$ .

Calculation:

The slope of the line is,

  $\begin{array}{c}m=\frac{y_2-y_1}{x_2-x_1}\\ =\frac{5-4}{2-1}\\ =1\end{array}$

The slope intercept form is,

  $y=mx+c$

Here, the slope is $m$ and $y$ intercept is $c$ .

Substitute the values in above equation.

  $\begin{array}{l}y=\left(1\right)x+c\\ y=x+c\end{array}$ ....................(1)

Substitute the values of point through which the line is passing in above equation.

  $\begin{array}{l}2=1+c\\ 2=1+c\\ c=1\end{array}$

Substitute the value in equation (1).

  $y=x+1$