Find the x-intercept and y-intercept of the line.=+5x4y−20x-intercept: y-intercept:

1. Break Down the Problem

We need to find the x-intercept and y-intercept of the line given by the equation $5x + 4y - 20 = 0$.

2. Relevant Concepts

• The x-intercept occurs where $y = 0$.
• The y-intercept occurs where $x = 0$.

3. Analysis and Detail

Finding the x-intercept:

1. Set $y = 0$ in the equation: $5x + 4(0) - 20 = 0$ Simplifying gives: $5x - 20 = 0$ Solving for $x$: $5x = 20 \implies x = \frac{20}{5} = 4$ Therefore, the x-intercept is $(4, 0)$.

Finding the y-intercept:

1. Set $x = 0$ in the equation: $5(0) + 4y - 20 = 0$ Simplifying gives: $4y - 20 = 0$ Solving for $y$: $4y = 20 \implies y = \frac{20}{4} = 5$ Therefore, the y-intercept is $(0, 5)$.

4. Verify and Summarize

• The x-intercept calculated as $(4, 0)$ is verified.
• The y-intercept calculated as $(0, 5)$ is also verified.

Final Answer

• x-intercept: $(4, 0)$
• y-intercept: $(0, 5)$