Chapter 1.1, Problem 53E

a.

To determine

Calculate the slope and y − intercept (if possible) for the linear equation.

Answer to Problem 53E

The slope of the equation is zero and the y− intercept is $(0,\frac{-5}{3})$ .

Explanation of Solution

Given:

It is given in the question that the equation is $3y+5=0$ .

Concept Used:

In this we have to keep some concept in mind:

(i) The graph of $y=mx+b$ is a straight line ,in which the slope is m and the y − intercept is $(0,b)$ .

(ii)Slope interceptform : $y=mx+b$

(iii) $m=\frac{rise}{sun}$

  (a)If $m>0$ ,the line rises from left to right.

  (b)If $m=0$ ,the line is horizontal.

  (c)If $m<0$ ,the line falls from left to right.

  (d)If m is undefined, the line is vertical.

Calculation: The given equation is, $3y+5=0$ .

  $\begin{array}{l}3y+5=0(solvingfory)\\ 3y=-5\\ y=\frac{-5}{3}\end{array}$

Since there is no x − value in this equation .

Here we see that , the slope is zero and the y − intercept is $(0,\frac{-5}{3})$

Conclusion:

The slope is zero and the y− intercept is $(0,\frac{-5}{3})$

b.

To determine

Sketch the line by hand and by using the graphing utility.

Explanation of Solution

Given:

It is given in the question that the equation is $3y+5=0$ and the slope is zero and the y − intercept is $(0,\frac{-5}{3})$ .

Graph:

  

Interpretation:

The equation $3y+5=0$ will put in the graphing calculator and it gives the graph and it also means that every point on the line has an y − value of $\frac{-5}{3}$ ,it also means that the line will never cross the x − axis.

So to draw this, pick a few y − values like $(0,\frac{-5}{3}),(2,\frac{-5}{3})and(-2,\frac{-5}{3})$ .