Chapter 4, Problem 6PT

To determine

To Find: The equation of the line in slope- intercept form passing through points $\left(7,-1\right)\&\left(9,-4\right)$ .

Answer to Problem 6PT

The equation of line in slope intercept form is $y=-\frac{3}{2}x+\frac{19}{2}$ .

Explanation of Solution

Given information:

Line passing through $\left(7,-1\right)\&\left(9,-4\right)$

Concept and Formula Used:

Equation of line passing through two points is given by $y-y_1=\left(\frac{y_2-y_1}{x_2-x_1}\right)\left(x-x_1\right)$ . Slope intercept form $y=mx+c$

Calculation:

It is given that line passing through $\left(7,-1\right)\&\left(9,-4\right)$

Equation of line through point and given slope is

  $\begin{array}{l}y-y_1=\left(\frac{y_2-y_1}{x_2-x_1}\right)\left(x-x_1\right)\\ \text{where }\left(x_1,y_1\right)=\left(7,-1\right)\&\left(x_2,y_2\right)=\left(9,-4\right)\\ y-\left(-1\right)=\left(\frac{-4-\left(-1\right)}{9-7}\right)\left(x-7\right)\\ y+1=\left(\frac{-4+1}{2}\right)\left(x-7\right)\\ y+1=-\frac{3}{2}(x-7)\\ y+1=-\frac{3}{2}x+\frac{21}{2}\\ y=-\frac{3}{2}x+\frac{21}{2}-1\\ y=-\frac{3}{2}x+\frac{21-2}{2}\\ y=-\frac{3}{2}x+\frac{19}{2}\end{array}$

Conclusion:

The equation of line in slope intercept form is $y=-\frac{3}{2}x+\frac{19}{2}$ .