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The image shows the following problem:

**(b) Find the equation of a line passing through the x-intercept 3 and y-intercept -5.**

To solve this, we can use the **two-intercept form of a line**. The general form for a line with x-intercept \(a\) and y-intercept \(b\) is given by:

\[
\frac{x}{a} + \frac{y}{b} = 1
\]

Here, \(a = 3\) (the x-intercept) and \(b = -5\) (the y-intercept). Substituting these values into the formula:

\[
\frac{x}{3} + \frac{y}{-5} = 1
\]

Multiplying through by 15 (the least common multiple of 3 and 5) to eliminate the denominators:

\[
5x - 3y = 15
\]

Thus, the equation of the line is:

\[
5x - 3y = 15
\]

Would you like further details on this solution or have any questions?

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Here are some related questions for practice:

1. How do you convert the equation \(5x - 3y = 15\) into slope-intercept form?
2. What is the slope of the line passing through these intercepts?
3. How do you find the slope of a line given two points?
4. How do you interpret the x-intercept and y-intercept of a line in a graph?
5. Can you use the same method to find the equation of a line passing through x-intercept -4 and y-intercept 6?

**Tip:** When given intercepts, always try to use the two-intercept form as a quick method to find the equation of the line.

Find the equation of a line passing through the x-intercept 3 and y-intercept -5.

This problem explores how to find the equation of a line passing through the x-intercept 3 and y-intercept -5 using the two-intercept form of a line. Learn the key steps and algebraic methods behind this problem, suitable for students in Grades 8-10.

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