To find the x- and y-intercepts of the line given by the equation \(5x - 4y = 40\), we can follow these steps:
X-Intercept
The x-intercept occurs when \(y = 0\). We can find it by substituting \(y = 0\) into the equation:
\[ 5x - 4(0) = 40 \]
This simplifies to:
\[ 5x = 40 \]
Now, divide both sides by 5:
\[ x = 8 \]
So, the x-intercept is \((8, 0)\).
Y-Intercept
The y-intercept occurs when \(x = 0\). We can find it by substituting \(x = 0\) into the equation:
\[ 5(0) - 4y = 40 \]
This simplifies to:
\[ -4y = 40 \]
Now, divide both sides by -4:
\[ y = -10 \]
So, the y-intercept is \((0, -10)\).
Summary
- X-Intercept: \((8, 0)\)
- Y-Intercept: \((0, -10)\)