Chapter 1.1, Problem 54E

a.

To determine

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

Answer to Problem 54E

The slope of the equation is zero and the y − intercept is $(0,-\frac{11}{4})$ .

Explanation of Solution

Given:

It is given in the question that the equation is $-11-4y=0$ .

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 intercept form : $y=mx+b$

(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, $-11-4y=0$ .

  $\begin{array}{l}-11-4y=0(solvingfory)\\ -4y=11\\ y=\frac{-11}{4}\end{array}$

Since there is no x − value in this equation .

Here it has seen that , the slope is zero and the y − intercept is $(0,-\frac{11}{4})$ .

Conclusion:

The slope is zero and the y − intercept is $(0,-\frac{11}{4})$ .

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 $-11-4y=0$ and the slope is zero and the y − intercept is $(0,-\frac{11}{4})$ .

Graph:

  

Interpretation:

The equation $-11-4y=0$ will be in the graphing calculator and it gives the graph and it also means that every point on the line has an y − value of $-\frac{11}{4}$ ,it also means that the line will never cross the x − axis and it is parallel to x − axis.