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The problem asks to write a slope-intercept equation for a line passing through the points \( (4,0) \) and \( (-5,3) \).

The slope-intercept form of a line is:
\[
y = mx + b
\]
where \( m \) is the slope and \( b \) is the y-intercept.

### Step 1: Find the slope (\( m \))
The formula for the slope between two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
Substitute \( (4,0) \) and \( (-5,3) \) into the formula:
\[
m = \frac{3 - 0}{-5 - 4} = \frac{3}{-9} = -\frac{1}{3}
\]

### Step 2: Use the point-slope form to find \( b \)
We can now use one of the points to solve for the y-intercept \( b \). Using the point \( (4,0) \), plug it into the slope-intercept form:
\[
0 = -\frac{1}{3}(4) + b
\]
\[
0 = -\frac{4}{3} + b
\]
\[
b = \frac{4}{3}
\]

### Final Equation
Now that we have the slope \( m = -\frac{1}{3} \) and the y-intercept \( b = \frac{4}{3} \), the equation of the line in slope-intercept form is:
\[
y = -\frac{1}{3}x + \frac{4}{3}
\]

Would you like any further details or explanations?

Here are five related questions to explore further:
1. How do you convert the slope-intercept form to the standard form of a line?
2. Can you derive the slope-intercept form from two different points?
3. How would the equation change if one of the points had a negative y-value?
4. How can you find the x-intercept of this line from the equation?
5. What does the slope tell you about the direction of the line?

**Tip**: Always ensure the slope calculation is correct by checking the change in both x and y directions.

Write a slope-intercept equation for a line that passes through (4,0) and (-5,3).

Learn how to find the slope-intercept equation of a line passing through the points (4,0) and (-5,3). This problem demonstrates how to calculate the slope and use it to write the equation of the line in slope-intercept form, suitable for students in Grades 8-10.

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