Chapter 1.1, Problem 44E

a.

To determine

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

Answer to Problem 44E

The slope of the equation is $m=\frac{-2}{3}$ and the y - intercept is $(0,3)$ .

Explanation of Solution

Given:

It is given in the question that the equation is $2x+3y-9=0$ .

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, $2x+3y-9=0$ .

  $\begin{array}{l}2x+3y-9=0(solvingfory)\\ 3y=-2x+9\\ y=\frac{-2x+9}{3}\\ y=\frac{-2}{3}x+3\end{array}$

Here it has seen that , $m=\frac{-2}{3}$ and the y − intersept is $(0,3)$ .

Conclusion:

The slope is $m=\frac{-2}{3}$ and the y − intersept is $(0,3)$ .

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 $2x+3y-9=0$ and the slope , $m=\frac{-2}{3}$ and the y − intersept is $(0,3)$ .

Graph:

  

Interpretation:

The equation $2x+3y-9=0$ will be put in the graphing calculator and it gives the graph and also keep in mind that we have to check that wether the line pass through the point $(0,3)$ or not.