Question

1. which function has a y-intercept of -2?

a) 2x - 2y = -4
b) 16x + 8y = -16
c) y = 2 - 2x
d) y - 3 = 2(x - 3)

Explanation:

Step1: Recall Y - intercept definition

The y - intercept of a function is the value of \(y\) when \(x = 0\). We will substitute \(x=0\) into each equation and solve for \(y\).

Step2: Analyze Option A (\(2x - 2y=-4\))

Substitute \(x = 0\) into the equation:
\(2(0)-2y=-4\)
Simplify: \(- 2y=-4\)
Divide both sides by \(-2\): \(y=\frac{-4}{-2} = 2\). So the y - intercept is \(2\), not \(-2\) (assuming the full question is about y - intercept of \(-2\), we will check other options).

Step3: Analyze Option B (\(16x + 8y=-16\))

Substitute \(x = 0\) into the equation:
\(16(0)+8y=-16\)
Simplify: \(8y=-16\)
Divide both sides by \(8\): \(y=\frac{-16}{8}=-2\).

Step4: Analyze Option C (\(y = 2-2x\))

Substitute \(x = 0\):
\(y=2 - 2(0)=2\). Y - intercept is \(2\).

Step5: Analyze Option D (\(y - 3=2(x - 3)\))

First, expand the right - hand side: \(y-3 = 2x-6\)
Then, solve for \(y\): \(y=2x - 6 + 3=2x-3\)
Substitute \(x = 0\): \(y=2(0)-3=-3\). Y - intercept is \(-3\).

Answer:

B. \(16x + 8y=-16\)