Chapter 4.3, Problem 4Q

To determine

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

Answer to Problem 4Q

Equation of line in slope intercept form is $y=-2x+1$

Explanation of Solution

Given: Points are $\left(-2,5\right)$ and $\left(1,-1\right)$

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 $\left(-2,5\right)$ and $\left(1,-1\right)$

Thus, equation of line is calculated by substituting the values in below equation:

  $\begin{array}{l}y-y_1=\frac{y_2-y_1}{x_2-x_1}\left(x-x_1\right)\\ y-\left(-1\right)=\frac{5-\left(-1\right)}{-2-1}\left(x-1\right)\\ y+1=\frac{5+1}{-2-1}\left(x-1\right)\\ y+1=\frac{6}{-3}\left(x-1\right)\\ y+1=-2\left(x-1\right)\\ y+1=-2x+2\\ y=-2x+1\end{array}$

Conclusion:

Hence, equation of line in slope intercept form is $y=-2x+1$