Chapter 8.7, Problem 60PFA

To determine

The equation $y-y_1=m\left(x-x_1\right)$ for the variable x .

Answer to Problem 60PFA

  $x=\frac{y-y_1+m{x}_1}{m}$

Explanation of Solution

Given information:

The point slope from of a line is given by $y-y_1=m\left(x-x_1\right)$ .

Concept Used:

• To get rid of a number in addition from one side, subtract the same number from both sides of equal sign.
• To get rid of a number in subtraction from one side, add the same number both sides of equal sign.
• To get rid of a number in multiplication from one side, divide the same number from both sides of equal sign.
• To get rid of a number in division from one side, multiply the same number both sides of equal sign.

Rules of Addition/ Subtraction:

• Two numbers with similar sign always get added and the resulting number will carry the similar sign.
• Two numbers with opposite signs always get subtracted and the resulting number will carry the sign of larger number.

Rules of Multiplication/ Division:

• The product/quotient of two similar sign numbers is always positive.
• The product/quotient of two numbers with opposite signs is always negative.

Calculation:

In order to solve for the variable x , first divide both sides by m and then add x1 both sides to simplify further as shown below:

  $\begin{array}{l}y-y_1=m\left(x-x_1\right)\\ \frac{y-y_1}{m}=\frac{m\left(x-x_1\right)}{m}\\ \frac{y-y_1}{m}=x-x_1\\ \frac{y-y_1}{m}+x_1=x-x_1+x_1\\ \frac{y-y_1+m{x}_1}{m}=x\\ x=\frac{y-y_1+m{x}_1}{m}\end{array}$

Thus, the formula for the variable is $x=\frac{y-y_1+m{x}_1}{m}$ .