Find the equation of the line with x-intercept 4 and y-intercept -5.

To find the equation of the line with an x-intercept of 4 and a y-intercept of -5, we'll use these intercepts to determine the slope and then write the equation in slope-intercept form \(y = mx + b\).

1. **Identify the points:**
   - The x-intercept is where the line crosses the x-axis, so the point is \((4, 0)\).
   - The y-intercept is where the line crosses the y-axis, so the point is \((0, -5)\).

2. **Find the slope (m):**
   The slope \(m\) is calculated by the formula:
   \[ m = \frac{y_2 - y_1}{x_2 - x_1} \]

   Using the points \((4, 0)\) and \((0, -5)\):
   \[ m = \frac{-5 - 0}{0 - 4} = \frac{-5}{-4} = \frac{5}{4} \]

3. **Write the equation in slope-intercept form:**
   The slope-intercept form of a line is:
   \[ y = mx + b \]

   We know the slope \(m = \frac{5}{4}\) and the y-intercept \(b = -5\), so:
   \[ y = \frac{5}{4}x - 5 \]

Thus, the equation of the line with an x-intercept of 4 and a y-intercept of -5 is:
\[ y = \frac{5}{4}x - 5 \]

Would you like more details or have any questions about this process?

Here are some related questions to expand your understanding:

1. How do you find the equation of a line given two points?
2. What is the point-slope form of a line, and when is it useful?
3. How can you convert an equation from point-slope form to slope-intercept form?
4. What is the significance of the slope in the context of a real-world problem?
5. How do you determine the x-intercept of a line given its equation?
6. Can a line have more than one x-intercept or y-intercept?
7. How do you graph a line using its intercepts?
8. What is the effect of changing the slope on the graph of a line?

**Tip:** When working with intercepts, always remember that the x-intercept has a y-coordinate of 0, and the y-intercept has an x-coordinate of 0.

Learn how to find the equation of a line with an x-intercept of 4 and a y-intercept of -5 using the slope-intercept form. This problem involves identifying intercepts, calculating the slope, and writing the equation in standard form. Suitable for students in Grades 7-9.

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