Chapter 7.5, Problem 1EE

a.

To determine

Construct the graph of the equation $y=2x+1$.

Find the slope and intercept.

Find the height of the line at $x=2$.

Answer to Problem 1EE

The slope of the equation $y=2x+1$ is 2 and intercept is 1.

The height of the line at $x=2$ is 5.

Explanation of Solution

From the given information, the equation is $y=2x+1$.

If $x=0$, then

$\begin{array}{c}y=2\left(0\right)+1\\ =1\end{array}$

If $x=1$, then

$\begin{array}{c}y=2\left(1\right)+1\\ =3\end{array}$

If $x=2$, then

$\begin{array}{c}y=2\left(2\right)+1\\ =5\end{array}$

If $x=3$, then

$\begin{array}{c}y=2\left(3\right)+1\\ =7\end{array}$

If $x=4$, then

$\begin{array}{c}y=2\left(4\right)+1\\ =9\end{array}$

The procedure for constructing a graph is as follows:

Procedure:

• Mark x along the horizontal and y along the vertical.
• Consider the x-coordinate as 0 and y-coordinate as 1.
• Locate the point.
• In the same way locate the points (1, 3), (2, 5), (3. 7), and (4, 9).

Then, the line is as follows:

The slope of the equation $y=2x+1$ is 2 and intercept is 1.

The height of the line at $x=2$ is

$\begin{array}{c}y=2\left(2\right)+1\\ =5\end{array}$

Thus, the height of the line at $x=2$ is 5.

b.

To determine

Construct the graph of the equation $y=\frac{1}{2}x+2$.

Find the slope and intercept.

Find the height of the line at $x=2$.

Answer to Problem 1EE

The slope of the equation $y=\frac{1}{2}x+2$ is $\frac{1}{2}$ and intercept is 2.

The height of the line at $x=2$ is 3.

Explanation of Solution

From the given information, the equation is $y=\frac{1}{2}x+2$.

If $x=0$, then

$\begin{array}{c}y=\frac{1}{2}\left(0\right)+2\\ =2\end{array}$

If $x=1$, then

$\begin{array}{c}y=\frac{1}{2}\left(1\right)+2\\ =2.5\end{array}$

If $x=2$, then

$\begin{array}{c}y=\frac{1}{2}\left(2\right)+2\\ =3\end{array}$

If $x=3$, then

$\begin{array}{c}y=\frac{1}{2}\left(3\right)+2\\ =3.5\end{array}$

If $x=4$, then

$\begin{array}{c}y=\frac{1}{2}\left(4\right)+2\\ =4\end{array}$

Consider the x-coordinate as 0 and y-coordinate as 2 and locate the point. In the same way locate the points $\left(1,2.5\right)$, $\left(2,3\right)$, $\left(3,3.5\right)$ and $\left(4,4\right)$.

Then, the line is as follows:

The slope of the equation $y=\frac{1}{2}x+2$ is $\frac{1}{2}$ and intercept is 2.

The height of the line at $x=2$ is

$\begin{array}{c}y=\frac{1}{2}\left(2\right)+2\\ =3\end{array}$

Thus, the height of the line at $x=2$ is 3.