Use the slope-intercept form to find the slope *m* and *y*-intercept *b* of the given line.

4*x* − 3*y* = 9 then graph

We are asked to find the slope (\(m\)) and the \(y\)-intercept (\(b\)) of the line given by the equation:

\[
4x - 3y = 9
\]

### Step 1: Rewrite the equation in slope-intercept form
The slope-intercept form of a line is:

\[
y = mx + b
\]

To do this, solve for \(y\) in terms of \(x\):

1. Start with the original equation:  
   \[
   4x - 3y = 9
   \]

2. Subtract \(4x\) from both sides:  
   \[
   -3y = -4x + 9
   \]

3. Divide everything by \(-3\):  
   \[
   y = \frac{-4}{-3}x + \frac{9}{-3}
   \]
   Simplifying:
   \[
   y = \frac{4}{3}x - 3
   \]

### Step 2: Identify the slope and y-intercept
Now that the equation is in the form \(y = mx + b\), we can see:

- The slope \(m = \frac{4}{3}\)
- The y-intercept \(b = -3\)

### Step 3: Graph the line
- **y-intercept**: Start at the point \((0, -3)\) on the y-axis.
- **Slope**: The slope \(\frac{4}{3}\) means that for every 3 units you move horizontally (to the right), you move 4 units vertically (up). So, from \((0, -3)\), move right 3 units and up 4 units to get the next point \((3, 1)\).

I can help visualize the graph as well if you'd like!

Would you like to see the graph? Also, do you want further details or have any questions?

Here are 5 related questions to expand on this concept:
1. How do you find the slope between two given points?
2. What is the relationship between parallel and perpendicular slopes?
3. How do you find the equation of a line given a point and a slope?
4. How do you convert from slope-intercept form to standard form?
5. How do you calculate the x-intercept of a line from its equation?

**Tip**: Always check the units of the slope — it’s a ratio of vertical change to horizontal change.

Use the slope-intercept form to find the slope m and y-intercept b of the given line. 4x − 3y = 9 then graph

Learn how to find the slope and y-intercept of the line 4x - 3y = 9 and graph it. This problem explains key algebra concepts such as the slope-intercept form (y = mx + b), with step-by-step instructions for identifying the slope and y-intercept. Suitable for students in Grades 8-10.

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