Question: Find the x- and y-intercepts of the graph: \( y = -\frac{4}{5}x - 4 \) [Graph of the line \( y…

Find the x- and y-intercepts of the graph: \( y = -\frac{4}{5}x - 4 \)

[Graph of the line \( y = -\frac{4}{5}x - 4 \) is shown on a coordinate plane with x and y axes ranging from -6 to 6.]

y-intercept: ( , )

x-intercept: ( , )

Solution

To find the x- and y-intercepts of the graph given by the equation \( y = \frac{4}{5}x - 4 \), follow these steps: First, find the y-intercept: The y-intercept occurs where \( x = 0 \). Substitute \( x = 0 \) into the equation: \[ y = \frac{4}{5}(0) - 4 \] Simplify: \[ y = -4 \] So, the y-intercept is \( (0, -4) \). Next, find the x-intercept: The x-intercept occurs where \( y = 0 \). Substitute \( y = 0 \) into the equation: \[ 0 = \frac{4}{5}x - 4 \] Add 4 to both sides: \[ 4 = \frac{4}{5}x \] Multiply both sides by \( \frac{5}{4} \) to solve for \( x \): \[ x = \frac{5}{4} \cdot 4 \] Simplify: \[ x = 5 \] So, the x-intercept is \( (5, 0) \). Therefore, the y-intercept is \( (0, -4) \) and the x-intercept is \( (5, 0) \).