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.