Chapter 4.2, Problem 38E

a.

To determine

Whether $y-\mathrm{intercept}(b)$ of the given graph will be negative or positive.

Answer to Problem 38E

  $y-\mathrm{intercept}(b)$ will be negative.

Explanation of Solution

Given Information:Graph with two points.

  $y-\mathrm{intercept}(b)$ will be negative. Connecting the two points with a line and extending it using a rule would make this clear.

b.

To determine

To estimate: The coordinates of two points and then to confirm the answer in part $a$ .

Answer to Problem 38E

It is verified that $y-\mathrm{intercept}$ is negative as mentioned in part $a$ .

Explanation of Solution

Given information:Graph with two points.

Calculation:

Point slope formula: $y-y_1=m(x-x_1)$

According to estimate points are $(4,1.8)$ and $(8,4)$ .

  $\begin{array}{l}m=\frac{4-1.8}{8-4}\\ m=\frac{2.2}{4}\\ m=\frac{11}{20}\end{array}$

Considering the point $(8,4)$ and substituting the values in point slope formula,

  $\begin{array}{l}y-4=\frac{11}{20}(x-8)\\ y-4=\frac{11}{20}x-\frac{44}{10}\\ y=\frac{11}{20}x-\frac{4}{10}\end{array}$ (Distributive property)

Putting $x=0$ to find $y-\mathrm{int}ercept$ ,

  $y=-0.4$

Thus, it is verified that $y-\mathrm{intercept}$ is negative as mentioned in part $a$ .