Chapter 3.1, Problem 58PPS

(a)

To determine

Draw a line on a coordinate plane with x & y − interest, x **minus; intercept and no y − intercept; No x − intercept and y − intercept.

Answer to Problem 58PPS

Exactly 2 x − intercepts and exactly 2 y − intercept is not a linear equation.

Explanation of Solution

Given:

Concept Used:

x − Intercept means where the graph crosses the x axis and y = 0.

y − Intercept means where the graph crosses the y axis and x = 0.

Let an equation: $y=2x+1$

To find x − intercept, plug in y = 0 and solve for x:

  $\begin{array}{l}y=2x+1\\ 0=2x+1[\text{Plug}\text{in}y=0]\\ 0-1=2x+1-1[\text{subtract}1\text{from}\text{both}\text{sides}]\\ -1=2x\\ \frac{-1}{2}=\frac{2x}{2}\\ x=-\frac{1}{2}\end{array}$ x − Intercept is $-\frac{1}{2}$

To find y − intercept, plug in x = 0 and solve for y:

  $\begin{array}{l}y=2x+1\\ y=2·0+1[\text{Plug}\text{in}x=0]\\ y=1\end{array}$ y- Intercept = 1

Equation: $y=2x+1$ and x − y intercepts are $-\frac{1}{2}\text{and}1$

  

x − Intercept and no y − intercept. This is a vertical line parallel to y − axis. The equation: $x=3$	No x − Intercept and y − intercept. This is a Horizontal line parallel to x − axis. The equation: $y=3$

(b)

To determine

Find the characteristics were you able to create a line for which characteristics were you unable to create a line.

Explanation of Solution

Given:

For which characteristics were you able to create a line for which characteristics were you unable to create a line. Explain.

Concept Used:

Exactly two x − intercepts and exactly two y − intercept is not a linear equation .They all are curved line. We cannot draw them as linear line.

Line: $y=2x+1$ is a linear equation. $x=3$ and $y=3$ are linear equation.

(c)

To determine

Find the meaning of x and y − intercepts.

Explanation of Solution

Given:

What must be true of the x − and y − intercept of a line?

Concept Used:

X − Intercepts means the line where crosses the x − axis. Similarly y − intercepts means the line where crosses the y − axis.

We can find the slope or inclination of the line from the x and y − intercepts.

Slope = $\frac{y-\text{intercept}}{x-\text{intercept}}$