It looks like you've uploaded an image of a worksheet titled
"Writing Equations of Lines" with teacher directions and an answer key. However, the actual image content isn't visible in this interface. Based on your description, I can help guide you through solving such problems and explain the solution process.
Let me walk you through how to solve typical problems like these:
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🔹 Task Overview:
The worksheet likely asks students to:
- Write the equation of a line in
slope-intercept form (\( y = mx + b \)) given:
- A point the line passes through
- Information about its relationship to another line (e.g., parallel or perpendicular)
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🔹 Key Concepts:
1.
Slope-Intercept Form:
\( y = mx + b \)
Where:
- \( m \) = slope
- \( b \) = y-intercept
2.
Parallel Lines:
Have
equal slopes.
3.
Perpendicular Lines:
Have slopes that are
negative reciprocals (i.e., if one slope is \( m \), the other is \( -\frac{1}{m} \)).
4.
Point-Slope Form (used for derivation):
\( y - y_1 = m(x - x_1) \)
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🔹 Example Problem:
Let’s assume one of the problems says:
>
Write the equation of the line that passes through (−1, 3) and is parallel to the line \( 2x + 5y = 15 \).
#### Step 1: Find the slope of the given line.
Rewrite \( 2x + 5y = 15 \) in slope-intercept form:
\[
5y = -2x + 15 \\
y = -\frac{2}{5}x + 3
\]
So, the slope \( m = -\frac{2}{5} \)
Since the new line is
parallel, it has the same slope: \( m = -\frac{2}{5} \)
#### Step 2: Use point-slope form with point (−1, 3):
\[
y - 3 = -\frac{2}{5}(x + 1)
\]
#### Step 3: Simplify to slope-intercept form:
\[
y - 3 = -\frac{2}{5}x - \frac{2}{5} \\
y = -\frac{2}{5}x - \frac{2}{5} + 3 \\
y = -\frac{2}{5}x + \frac{13}{5}
\]
✔ Final Answer: \( y = -\frac{2}{5}x + \frac{13}{5} \)
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🔹 How to Match & Color Code (as per instructions):
- Students write their equations.
- They match them to the correct equation listed in the "Answer Key" section.
- Then they color the corresponding number in the grid using a specific color.
This type of activity helps reinforce understanding while making practice engaging.
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🔹 Common Mistakes to Avoid:
- Confusing parallel vs. perpendicular slopes
- Forgetting to distribute when simplifying
- Misidentifying the slope from standard form
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If you can describe or list the specific problems from the worksheet, I can solve each one step-by-step and provide the exact answers.
Would you like to share the text of the problems or any specific ones you're stuck on?
Parent Tip: Review the logic above to help your child master the concept of writing equations of parallel and perpendicular lines worksheet answer key.
