Chapter 8.3, Problem 20PSB

a

To determine

To calculate: Slope of the line

Answer to Problem 20PSB

Slope of line is $\frac{-1}{12}$ .

Explanation of Solution

Given information : Here, we have given a line with two coordinates $(-9,7)$ and $(3,1)$ .

Formula used : Slope of line = $\frac{{\text{y}}_{\text{2}}{\text{-y}}_{\text{1}}}{{\text{x}}_{\text{2}}{\text{-x}}_{\text{1}}}$ .

Calculation: As, Coordinates of line are $(-9,7)$ and $(3,1)$ ,

  $\Rightarrow {\text{x}}_{\text{1}}=-9$ , ${\text{x}}_{\text{2}}=3$ , $y_1=7$ and ${\text{y}}_{\text{2}}=1$

As, slope of line is $\frac{{\text{y}}_{\text{2}}{\text{-y}}_{\text{1}}}{{\text{x}}_{\text{2}}{\text{-x}}_{\text{1}}}$ ,

  $\begin{array}{l}\Rightarrow \frac{1-7}{3-(-9)}\\ \Rightarrow \frac{-6}{3+9}\\ \Rightarrow \frac{-6}{12}\\ \Rightarrow \frac{-1}{12}\end{array}$

b

To determine

To calculate: Value of y will increase or decrease

Answer to Problem 20PSB

Values of y will decrease by $\frac{-1}{6}$ times.

Explanation of Solution

Given information : Here, we have given that x values of the point increase by 3.

Formula used : Slope of line = $\frac{{\text{y}}_{\text{2}}{\text{-y}}_{\text{1}}}{{\text{x}}_{\text{2}}{\text{-x}}_{\text{1}}}$ .

Calculation: As, Coordinates of line are $(-9,7)$ and $(3,1)$ ,

  $\Rightarrow {\text{x}}_{\text{1}}=-9$ , ${\text{x}}_{\text{2}}=3$

Now, as values of x increase by 3,

  $\Rightarrow x_1=-9+3=-6$ and $\Rightarrow {\text{x}}_{\text{2}}=3+3=6$

As, slope of line is $\frac{-1}{2}$ . (Calculated above)

  $\begin{array}{l}\Rightarrow \frac{-1}{2}=\frac{{\text{y}}_{\text{2}}{\text{-y}}_{\text{1}}}{\text{6-(-6)}}\\ \Rightarrow \frac{-1}{2}=\frac{{\text{y}}_{\text{2}}{\text{-y}}_{\text{1}}}{\text{12}}\\ \Rightarrow -12=2{\text{(y}}_{\text{2}}{\text{-y}}_{\text{1}}\text{)}\\ \Rightarrow \frac{-2}{12}{\text{(y}}_{\text{2}}{\text{-y}}_{\text{1}}\text{)}\\ \Rightarrow \frac{-1}{6}{\text{(y}}_{\text{2}}{\text{-y}}_{\text{1}}\text{)}\end{array}$

  $\therefore$ Values of y will decrease by $\frac{-1}{6}$ times.