Chapter 4.2, Problem 38E

(a)

To determine

To explain: the linear function appear to be positive or negative.

Answer to Problem 38E

The y -intercept of the graph of linear function appear to be negative.

Explanation of Solution

Given:

Consider the graph shows two points that lie on the graph of a linear function

  

Calculation:

Draw the line joining the two points on the graph.

As from the graph line is a cut the y axis below the x axis.

So, the y -intercept of the graph of linear function appear to be negative.

Conclusion:

Therefore, the y -intercept of the graph of linear function appear to be negative.

(b)

To determine

To estimate: the coordinates of the two points and use your estimates to confirm your answer in part (a).

Answer to Problem 38E

The estimate of the point coordinates are confirm.

Explanation of Solution

Calculation:

Estimate the coordinates of the points

From the graph the coordinates of the points are $\left(4,1.7\right)$ and $\left(8,4\right)$

Now, to confirm the estimate of the point coordinates, use these points and find the slope

  $\begin{array}{l}m=\frac{y_2-y_1}{x_2-x_1}\\ =\frac{4-1.7}{8-4}\\ =0.575\end{array}$

Now, use the slope $m=0.575$ and the point $\left(8,4\right)$ to write the slope-point equation

  $\begin{array}{l}y-y_1=m\left(x-x_1\right)\\ y-4=\left(0.575\right)\left(x-8\right)\\ y-4=0.575x-4.6\end{array}$

Add 4 on both sides

  $y=0.575x-0.6$

Now, from the equation it is clear that the y -intercept is negative

Conclusion:

Therefore, the estimate of the point coordinates are confirm.