Question

6.1 ws: converting point - slope to slope - intercept
write the slope - intercept form of the equation of each line.

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

a) $y = -x - 4$ b) $y = 8x - 4$ c) $y = -4x - 1$ d) $y = -8x - 4$

1. $y + 4 = -(x - 4)$

a) $y = 1$ b) $y = x$ c) $y = -x$ d) $y = x + 1$

Explanation:

Problem 1: \( y - 3 = 7(x - 2) \)

Step 1: Distribute the 7

\( y - 3 = 7x - 14 \)

Step 2: Add 3 to both sides

\( y = 7x - 14 + 3 \)
\( y = 7x - 11 \)

Step 1: Distribute the -2

\( y + 3 = -2x + 6 \)

Step 2: Subtract 3 from both sides

\( y = -2x + 6 - 3 \)
\( y = -2x + 3 \)

Step 1: Distribute the \( \frac{5}{2} \)

\( y + 3 = \frac{5}{2}x + 10 \)

Step 2: Subtract 3 from both sides

\( y = \frac{5}{2}x + 10 - 3 \)
\( y = \frac{5}{2}x + 7 \)

Answer:

\( y = 7x - 11 \)

Problem 2: \( y + 3 = -2(x - 3) \)