Chapter 6.7, Problem 62SR

To determine

To write: The slope intercepts form for the line

Answer to Problem 62SR

The slope intercept form of the line is $y=x+5$

Explanation of Solution

Given:

Equation: $y=x-6$

Point: $(-3,2)$

Calculation:

If the equation of the line is $y=mx+c$ then slope of the line is $m$

Required line is parallel to the line with equation $y=x-6$

Since slope of parallel line is same, thus slope of the required line is $1$

Required line passes through the point $(-3,2)$ and has slope $1$

Therefore the equation of the line is given by

  $\begin{array}{l}\frac{y-2}{x-(-3)}=1\\ \frac{y-2}{x+3}=1\\ y-2=1(x+3)\\ y-2=x+3\\ y=x+3+2\\ y=x+5\end{array}$

Conclusion:

Hence, the slope intercept form of the line is $y=x+5$