Let’s solve both problems step by step.
---
Problem 1: Write the equation of a line that is parallel to y = 4x + 9 and passes through (0,2)
Step 1: Parallel lines have the same slope.
The given line is y = 4x + 9 → slope m = 4
So our new line also has m = 4
Step 2: We are given point (0,2) → x = 0, y = 2
Step 3: Plug into y = mx + b
→ 2 = 4(0) + b
→ 2 = 0 + b
→ b = 2
Step 4: Now write the full equation using m = 4 and b = 2
→ y = 4x + 2
✔ Final Answer for Problem 1:
y = 4x + 2
---
Problem 2: Write the equation of a line that is perpendicular to y = -6x + 12 and passes through (12, -5)
Step 1: Perpendicular lines have opposite reciprocal slopes.
Given line: y = -6x + 12 → slope = -6
Opposite reciprocal of -6 is:
→ Flip the fraction: -6 = -6/1 → flip to -1/6
→ Then change sign: becomes
+1/6
So our new slope m = 1/6
Step 2: Given point (12, -5) → x = 12, y = -5
Step 3: Plug into y = mx + b
→ -5 = (1/6)(12) + b
→ -5 = 2 + b
→ Subtract 2 from both sides:
→ -5 - 2 = b
→ b = -7
Step 4: Write full equation with m = 1/6 and b = -7
→ y = (1/6)x - 7
✔ Final Answer for Problem 2:
y = (1/6)x - 7
---
Final Answer:
For the parallel line:
y = 4x + 2
For the perpendicular line:
y = (1/6)x - 7
Parent Tip: Review the logic above to help your child master the concept of writing equations of parallel and perpendicular lines worksheet answer key.
