Question

find the y-intercept and x-intercept of the line.
4x - 3y = 9
y-intercept:
x-intercept:

Explanation:

Step1: Find y - intercept

To find the y - intercept, we set \(x = 0\) in the equation \(4x-3y = 9\).
Substituting \(x = 0\) into the equation, we get \(4(0)-3y=9\), which simplifies to \(- 3y=9\).
Dividing both sides by \(-3\), we have \(y=\frac{9}{-3}=- 3\).

Step2: Find x - intercept

To find the x - intercept, we set \(y = 0\) in the equation \(4x-3y = 9\).
Substituting \(y = 0\) into the equation, we get \(4x-3(0)=9\), which simplifies to \(4x=9\).
Dividing both sides by \(4\), we have \(x=\frac{9}{4}\).

Answer:

y - intercept: \(-3\)
x - intercept: \(\frac{9}{4}\)