Chapter 4.2, Problem 4AGP

To determine

To calculate: An equation in point-slope form and standard form the line containing side $\overline{ST}$ .

Answer to Problem 4AGP

Equation in slope-intercept form is $y=-x+12.$

Equation in standard form is $x+y=12.$

Explanation of Solution

Given information:The figure shows square RSTU.

Calculation:

The coordinates of point S is (4,8) $(x_1,y_1)$ .

The coordinates of point T is (7,5) $(x_2,y_2)$ .

So, the slope of the line $\overline{ST}$ is ,

  $m=\frac{y_2-y_1}{x_2-x_1}=\frac{5-8}{7-4}=\frac{-3}{3}=-1$ .

Substitute the point S(4,8) and the slope m =-1 into the slope-intercept form of a line and solve for b .

  $\begin{array}{l}y=mx+b.\\ 8=-1\times 4+b.\\ b=8+4=12.\end{array}$

Substitute the slope m =-1 and b =12 into slope-intercept form of a line.

  $\begin{array}{l}y=-1\times x+12.\\ y=-x+12.\end{array}$

So, equation in slope-intercept form is ,

  $y=-x+12.$

In standard form the equation is ,

  $x+y=12.$