Chapter 8, Problem 10PT

To determine

To state: the slope and y-intercept of the graph

Answer to Problem 10PT

The slope is $-\frac{4}{3}$ and the y intercept is 2

Explanation of Solution

Given:

Consider the equation: $4x+3y=6$

Calculation:

The general form of equation of line in slope intercept form is:

  $y=mx+b$

Here, m represents slope intercept and b stands for y intercept.

Subtract both sides of equation by $4x$

  $\begin{array}{c}4x+3y-4x=-4x+6\\ 3y=-4x+6\end{array}$

Divide both sides of equation by 3.

  $\begin{array}{c}\frac{3y}{3}=\frac{-4x+6}{3}\\ y=-\frac{4}{3}x+2\end{array}$

Hence, the equation $y=-\frac{4}{3}x+2$ is written in the form of $y=mx+b$

Since, we get the slope and y intercept. Now, graph the y intercept point at $\left(0,2\right)$

  

Now, use the value of slope to locate the second point.

As, slope is change in y with respect to change in x

Since, slope is $-\frac{4}{3}$

Move 4 units down and 3 unit right from y intercept to get another point.

So, draw a line through the two points.

  

Conclusion:

The slope is $-\frac{4}{3}$ and the y intercept is 2