Question

y = mx+b
write the following equation in slope intercept form:
y - 2 = -4(x - 3)
options:
y = -4x + 14
y = -4x - 10
y = -4x + 10
y = -4x - 14

Explanation:

Step1: Expand the right side

Using the distributive property \(a(b - c)=ab - ac\), for \(-4(x - 3)\), we get \(-4x+12\). So the equation becomes \(y - 2=-4x + 12\).

Step2: Solve for y

Add 2 to both sides of the equation. \(y-2 + 2=-4x+12 + 2\), which simplifies to \(y=-4x + 14\). Wait, no, wait: \(12 + 2 = 14\)? Wait, no, wait, let's recalculate. Wait, \(-4\times(-3)=12\), then \(y-2=-4x + 12\), then add 2: \(y=-4x+12 + 2\)? Wait, no, 12 + 2 is 14? But wait, let's check again. Wait, the original equation is \(y - 2=-4(x - 3)\). Distribute \(-4\) into \((x - 3)\): \(-4\times x=-4x\), \(-4\times(-3)=12\). So \(y - 2=-4x + 12\). Then add 2 to both sides: \(y=-4x+12 + 2\)? Wait, no, 12 + 2 is 14? But wait, the third option is \(y=-4x + 10\). Wait, I must have made a mistake. Wait, no: \(y - 2=-4(x - 3)\). Let's do it again. \(-4(x - 3)=-4x+12\). Then \(y-2=-4x + 12\). Add 2 to both sides: \(y=-4x+12 + 2\)? Wait, no, 12 + 2 is 14? But the options have \(y=-4x + 14\) as the first option and \(y=-4x + 10\) as the third. Wait, maybe I miscalculated the distribution. Wait, \(-4(x - 3)\): \(x-3\) times -4: \(-4\times x=-4x\), \(-4\times(-3)=12\). Then \(y - 2=-4x + 12\). Then add 2: \(y=-4x+12 + 2\)? Wait, 12 + 2 is 14. But let's check with the point. Let's take x = 3, then original equation: \(y - 2=-4(3 - 3)=0\), so \(y=2\). Now plug x = 3 into \(y=-4x + 14\): \(y=-12 + 14 = 2\), which matches. Plug x = 3 into \(y=-4x + 10\): \(y=-12 + 10=-2\), which doesn't match. Wait, so my first calculation was right. But wait, the third option is \(y=-4x + 10\). Wait, maybe I made a mistake in the problem. Wait, no, the original equation is \(y - 2=-4(x - 3)\). Let's expand again: \(y-2=-4x + 12\), then \(y=-4x+14\). So the first option is \(y=-4x + 14\), but wait, the user's options: first option is \(y=-4x + 14\), second is \(y=-4x - 10\), third is \(y=-4x + 10\), fourth is \(y=-4x - 14\). Wait, but when x = 3, y should be 2. Let's check \(y=-4x + 14\) at x = 3: \(-12 + 14 = 2\), correct. \(y=-4x + 10\) at x = 3: \(-12 + 10=-2\), incorrect. So why is there a discrepancy? Wait, maybe I misread the original equation. Wait, the original equation is \(y - 2=-4(x - 3)\)? Or is it \(y - 2=-4(x + 3)\)? No, the user wrote \(y - 2=-4(x - 3)\). So according to that, the correct answer is \(y=-4x + 14\), which is the first option. But wait, let's check again. Wait, \(-4(x - 3)=-4x + 12\), then \(y-2=-4x + 12\), so \(y=-4x + 14\). Yes, that's correct.

Answer:

A. \(y = -4x + 14\)