Chapter 1.1, Problem 35E

To determine

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

Answer to Problem 35E

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 $2x-3y=9$ .

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, $2x-3y=9$ .

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

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

The slope is $m=\frac{2}{3}$ that defines that the line of the graph falls from left to right.

Conclusion:

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