Question

1. determine the coordinates of the x-intercept of 3x - 4y = 24.

a. (8, 0)
b. (0, 8)
c. (-6, 0)
d. (0, -6)

Explanation:

Step1: Recall x-intercept definition

The x - intercept of a line is the point where the line crosses the x - axis. At this point, the y - coordinate is 0. So we set \(y = 0\) in the equation \(3x-4y = 24\).

Step2: Substitute \(y = 0\) into the equation

Substitute \(y = 0\) into \(3x-4y=24\), we get \(3x-4\times0 = 24\), which simplifies to \(3x=24\).

Step3: Solve for x

To solve for \(x\), divide both sides of the equation \(3x = 24\) by 3. So \(x=\frac{24}{3}=8\).
Since \(y = 0\) and \(x = 8\), the coordinates of the x - intercept are \((8,0)\).

Answer:

A. \((8, 0)\)