Chapter 4.3, Problem 5Q

To determine

To calculate: To write the equation of line in slope intercept form that passes through the given points

Answer to Problem 5Q

Equation of line in slope intercept form is $y=\frac{x}{5}-\frac{7}{5}$

Explanation of Solution

Given: Points are $\left(-3,-2\right)$ and $\left(2,-1\right)$

Formula Used:

Equation of line in slope intercept form is given as:

  $y=mx+c$ , where $\begin{array}{l}m=slope\\ c=y-intercept\end{array}$

Also, equation of line passing through two points is given as

  $y-y_1=\frac{y_2-y_1}{x_2-x_1}\left(x-x_1\right)$

Calculation:

Given that the line passes through the points $\left(-3,-2\right)$ and $\left(2,-1\right)$

Thus, equation of line is calculated as follows:

  $y-y_1=\frac{y_2-y_1}{x_2-x_1}\left(x-x_1\right)$

Substituting the values in above equation:

  $\begin{array}{l}y-\left(-1\right)=\frac{-2-\left(-1\right)}{-3-2}\left(x-2\right)\\ y+1=\frac{-2+1}{-3-2}\left(x-2\right)\\ y+1=\frac{-1}{-5}\left(x-2\right)\\ 5\left(y+1\right)=1\left(x-2\right)\\ 5y+5=x-2\\ 5y=x-7\\ y=\frac{x}{5}-\frac{7}{5}\end{array}$

Conclusion:

Hence, equation of line in slope intercept form is $y=\frac{x}{5}-\frac{7}{5}$