Question

find the y-intercept and x-intercept of the line.
5x - 7y = -12
y-intercept:
x-intercept:

Explanation:

Step1: Find y - intercept (set \(x = 0\))

Substitute \(x = 0\) into the equation \(5x-7y=-12\).
We get \(5(0)-7y=-12\), which simplifies to \(-7y=-12\).
To solve for \(y\), divide both sides by \(-7\): \(y=\frac{-12}{-7}=\frac{12}{7}\).

Step2: Find x - intercept (set \(y = 0\))

Substitute \(y = 0\) into the equation \(5x - 7y=-12\).
We get \(5x-7(0)=-12\), which simplifies to \(5x=-12\).
To solve for \(x\), divide both sides by \(5\): \(x =-\frac{12}{5}\).

Answer:

y - intercept: \(\frac{12}{7}\)
x - intercept: \(-\frac{12}{5}\)