Chapter 9.3, Problem 26IP

To determine

To calculate: Value of p.

Answer to Problem 26IP

Value of p is $1$ .

Explanation of Solution

Given information:

The following points:

  $\text{(0,}p\text{),(1,4)}$

Slope of the line = $3$

Formula used:

Slope is given by the formula,

  $m=\frac{y_2-y_1}{x_2-x}$

where $x_2\ne x$ .

Calculation:

Use the formula for calculating slope to find the value of p.

Value of p is calculated as follows:

  $\begin{array}{l}m=\frac{y_2-y_1}{x_2-x}[\text{Definition of slope]}\\ 3=\frac{4-p}{1-0}[(x_1,y_1)=(0,p),(x_2,y_2)=(1,4),m=3]\\ 3=4-p[\text{Simplify]}\\ 3+p=4-p+p[\text{Add }p\text{ to both sides]}\\ 3+p=4[\text{Simplify]}\\ \text{3}+p-3=4-3[\text{Subtract 3 from both sides]}\\ p=1[\text{Simplify]}\end{array}$