To find the x- and y-intercepts of the line represented by the equation \(5x - 4y = 40\), we can set up the following calculations:
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Finding the x-intercept: The x-intercept occurs when \(y = 0\).
Substitute \(y = 0\) into the equation: \[ 5x - 4(0) = 40 \implies 5x = 40 \implies x = \frac{40}{5} = 8 \] Thus, the x-intercept is \((8, 0)\).
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Finding the y-intercept: The y-intercept occurs when \(x = 0\).
Substitute \(x = 0\) into the equation: \[ 5(0) - 4y = 40 \implies -4y = 40 \implies y = \frac{40}{-4} = -10 \] Thus, the y-intercept is \((0, -10)\).
Summary:
- The x-intercept is \((8, 0)\).
- The y-intercept is \((0, -10)\).