Question

1. $y - 11 = 3(x + 4)$
2. $y + 5 = -6(x + 7)$
3. $y + 2 = \frac{1}{6}(x - 4)$
4. $y + 6 = -\frac{3}{4}(x + 8)$

Explanation:

Assuming the task is to convert these point - slope form equations to slope - intercept form (\(y = mx + b\)):

Problem 5: \(y - 11=3(x + 4)\)

Step 1: Distribute the 3

We use the distributive property \(a(b + c)=ab+ac\). Here, \(a = 3\), \(b=x\) and \(c = 4\). So we get \(y-11 = 3x+12\).

Step 2: Solve for \(y\)

Add 11 to both sides of the equation. \(y=3x + 12+11\), which simplifies to \(y=3x + 23\).

Problem 6: \(y + 5=-6(x + 7)\)

Step 1: Distribute the - 6

Using the distributive property \(a(b + c)=ab + ac\) with \(a=-6\), \(b = x\) and \(c = 7\), we have \(y + 5=-6x-42\).

Step 2: Solve for \(y\)

Subtract 5 from both sides. \(y=-6x-42 - 5\), so \(y=-6x-47\).

Problem 8: \(y + 2=\frac{1}{6}(x - 4)\)

Step 1: Distribute the \(\frac{1}{6}\)

Using the distributive property \(a(b - c)=ab-ac\) with \(a=\frac{1}{6}\), \(b=x\) and \(c = 4\), we get \(y + 2=\frac{1}{6}x-\frac{4}{6}\). Simplify \(\frac{4}{6}=\frac{2}{3}\), so \(y + 2=\frac{1}{6}x-\frac{2}{3}\).

Step 2: Solve for \(y\)

Subtract 2 from both sides. \(y=\frac{1}{6}x-\frac{2}{3}-2\). Since \(2=\frac{6}{3}\), we have \(y=\frac{1}{6}x-\frac{2}{3}-\frac{6}{3}=\frac{1}{6}x-\frac{8}{3}\).

Problem 9: \(y + 6=-\frac{3}{4}(x + 8)\)

Step 1: Distribute the \(-\frac{3}{4}\)

Using the distributive property \(a(b + c)=ab+ac\) with \(a =-\frac{3}{4}\), \(b=x\) and \(c = 8\), we get \(y + 6=-\frac{3}{4}x-6\).

Step 2: Solve for \(y\)

Subtract 6 from both sides. \(y=-\frac{3}{4}x-6 - 6\), so \(y=-\frac{3}{4}x-12\).

Answer:

s:

1. \(y = 3x+23\)
2. \(y=-6x - 47\)
3. \(y=\frac{1}{6}x-\frac{8}{3}\)
4. \(y =-\frac{3}{4}x-12\)