Chapter 12, Problem 86CUR

To determine

To write: the equation of line through $\left(0,5\right),\left(6,12\right)$

Answer to Problem 86CUR

The equation of line through $\left(0,5\right),\left(6,12\right)$ is $6y=7y+30$

Explanation of Solution

Given information:

Given points: $\left(0,5\right),\left(6,12\right)$

Formula used:

Slope formula:$slope(m)=\frac{changeiny}{change\text{ in }x}$

Equation of line:$y-y_1=m(x-x_1)$

Calculation:

  $\begin{array}{l}m=\frac{changeiny}{change\text{ in }x}\\ m=\frac{y_2-y_1}{x_2-x_1}\\ m=\frac{12-5}{6-0}\left[\text{substitute values of }{x}_1,x_2,y_1,y_2\right]\\ m=\frac{7}{6}\\ \text{create equation of line using1st point}\\ y-y_1=m(x-x_1)\\ y-5=\frac{7}{6}(x-0)\left[\text{substituting values of }{x}_1\text{ and }{y}_{{}_1}\right]\\ y-5=\frac{7x}{6}\left[\text{multiply}\right]\\ y=\frac{7x}{6}+5\left[\text{add 5 to both sides}\right]\\ 6y=7x+30\left[\text{multiply both sides by 6}\right]\end{array}$

Therefore,

The required equation of line is $6y=7x+30$