Chapter 13, Problem 9RP

(a)

To determine

To find: The equation of the line for the given condition.

Answer to Problem 9RP

The equation of the line is $y-1=2x$ .

Explanation of Solution

Given:

The slope is 2 and the y intercept is 1

Calculation:

Consider the general form for the equation of the line is,

  $y-y_1=m\left(x-x_1\right)$

Then, from the given data the equation of the line is,

  $\begin{array}{l}y-1=2\left(x-0\right)\\ y-1=2x\end{array}$

(b)

To determine

To find: The equation of the line for the given condition.

Answer to Problem 9RP

The equation of the line is $x=2$ .

Explanation of Solution

Given:

The two points of the line is $\left(2,3\right),\left(2,7\right)$ .

Calculation:

The formula to determine the slope of the line is of the form,

  $m=\frac{y_2-y_1}{x_2-x_1}$

Then, slope of the line with the points $\left(2,3\right),\left(2,7\right)$ is,

  $\begin{array}{c}m=\frac{7-3}{2-2}\\ =\infty \end{array}$

The above slope is the special case that denotes the perfectly vertical slope or the infinite slope. Thus, the equation of the line is,

  $x=2$

(c)

To determine

To find: The equation of the line for the given condition.

Answer to Problem 9RP

The equation of the line is $x+5=0$ .

Explanation of Solution

Given:

The line is parallel to and 5 points to the left of the y axis.

Calculation:

Consider the general form for the equation of the line is,

  $y-y_1=m\left(x-x_1\right)$

The line is parallel to the y axis then the value of y is 0.

  $\begin{array}{l}0=m\left(x-x_1\right)\\ x-x_1=0\end{array}$

The point is 5 point to the left of the y axis that is,

  $\begin{array}{l}x-\left(-5\right)=0\\ x+5=0\end{array}$

(d)

To determine

To find: The equation of the line for the given condition.

Answer to Problem 9RP

The equation of the line is $y-3x+2=0$ .

Explanation of Solution

Given:

The line passes through the points.

Calculation:

The formula to determine the slope of the line is of the form,

  $m=\frac{y_2-y_1}{x_2-x_1}$

Then, slope of the line with the points $\left(2,4\right),\left(6,16\right)$ is,

  $\begin{array}{c}m=\frac{16-4}{6-2}\\ =3\end{array}$

Consider the general form for the equation of the line is,

  $y-y_1=m\left(x-x_1\right)$

Then,

  $\begin{array}{l}y-4=3\left(x-2\right)\\ y-4=3x-6\\ y-3x+2=0\end{array}$

(e)

To determine

To find: The equation of the line for the given condition.

Answer to Problem 9RP

The equation of the line is $y=\frac{x}{2}-2$ .

Explanation of Solution

Given:

The slope is $\frac{1}{2}$ and x intercept is 4.

Calculation:

Consider the general form for the equation of the line is,

  $y-y_1=m\left(x-x_1\right)$

Then,

  $\begin{array}{l}y-0=\frac{1}{2}\left(x-4\right)\\ y=\frac{x}{2}-2\end{array}$

(f)

To determine

To find: The equation of the line for the given condition.

Answer to Problem 9RP

The equation of the line is $y+7=3x$ .

Explanation of Solution

Given:

The graph is parallel to the line $y=3x+1$ with the same $y$ intercept as the graph of $y=2x-7$ .

Calculation:

Consider the general form of the equation of the line is,

  $y=mx+c$

The equation of the line to be found is same as the slope of the line $y=3x+1$ that is 3.

The intercept of the line $y=2x-7$ is, than the equation of the line is,

  $y+7=3x$

(g)

To determine

To find: The equation of the line for the given condition.

Answer to Problem 9RP

The equation of the line is $y+3=\frac{1}{2}\left(x-6\right)$ .

Explanation of Solution

Given:

The intercept x is 6 and intercept y is $-3$ .

Calculation:

Consider the general form of the equation of the line is,

  $y=mx+c$

The slope of the equation is,

  $\begin{array}{c}m=-\left(\frac{-3}{6}\right)\\ =\frac{1}{2}\end{array}$

Then, the equation of the line is,

  $y+3=\frac{1}{2}\left(x-6\right)$