To solve the problem and graph the line represented by the equation $3x + 5y = 15$, we need to find the x-intercept and y-intercept.

Finding the Intercepts

1. X-intercept:

   • The x-intercept occurs when $y = 0$.
   • Substitute $y = 0$ into the equation $3x + 5y = 15$: $3x + 5(0) = 15 \implies 3x = 15 \implies x = 5$
   • The x-intercept is $(5, 0)$.

2. Y-intercept:

   • The y-intercept occurs when $x = 0$.
   • Substitute $x = 0$ into the equation $3x + 5y = 15$: $3(0) + 5y = 15 \implies 5y = 15 \implies y = 3$
   • The y-intercept is $(0, 3)$.

Plotting the Points and Graphing the Line

1. Plot the x-intercept $(5, 0)$ on the graph.
2. Plot the y-intercept $(0, 3)$ on the graph.
3. Draw a line through these two points to represent the equation $3x + 5y = 15$.

Here's a detailed solution:

• The x-intercept is at point $(5, 0)$.
• The y-intercept is at point $(0, 3)$.
• Use these two points to draw the line.

Would you like further details or have any questions about the process? Here are some related questions to consider:

1. How do you find the x-intercept and y-intercept of a different linear equation?
2. What are the steps to convert a linear equation into slope-intercept form?
3. How can you determine if a point lies on the line given by a linear equation?
4. What are the characteristics of parallel and perpendicular lines in terms of their slopes?
5. How do you graph a line given its slope and one point on the line?

Tip: Always verify your intercepts by substituting back into the original equation to ensure accuracy.