Chapter 4.1, Problem 37E

To determine

To show: that equation of the line that passes through the point $(0,b)$ and $(1,b+m)$ is , Also show that the point $(-1,b-m)$ lie on given line.

Answer to Problem 37E

The equation of line is $y=mx+b$ .

Explanation of Solution

Given Information: - We are given the points $(0,b)$ and $(1,b+m)$ , And equation $y=mx+b$ .

Calculation:

Slope of the line where is passing through the points $(0,b)$ and $(1,b+m)$

  $m=\frac{y_2-y_1}{x_2-x_1}$

  $\begin{array}{l}=\frac{b+m-b}{1-0}\\ =m\end{array}$

Equation of line in point slope form

  $\begin{array}{l}y-y_1=m(x-x_1)\\ y-b=m(x-0)\\ y-b=mx\\ y=mx+b\end{array}$

Point $(-1,b-m)$

Put $x=-1$ and $y=b-m$ on the equation $y=mx+b$

  $\begin{array}{l}b-m=m(-1)+b\\ b-m=-m+b\end{array}$

  $=b-m$

This shows that $(-1,b-m)$ also lie on line $y=mx+b$ .