You're working on
writing linear equations given a point and a slope, using the
point-slope formula:
>
Point-Slope Formula:
> \( y - y_1 = m(x - x_1) \)
Then, you must
distribute and
solve for y to get the equation in
slope-intercept form:
> \( y = mx + b \)
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Let’s solve problems
3 and
4 from your worksheet.
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✔ Problem 3: Point (-6, 0); slope = \( \frac{2}{3} \)
Step 1: Plug into point-slope formula
\( y - y_1 = m(x - x_1) \)
→ \( y - 0 = \frac{2}{3}(x - (-6)) \)
→ \( y = \frac{2}{3}(x + 6) \)
Step 2: Distribute the slope
\( y = \frac{2}{3}x + \frac{2}{3} \cdot 6 \)
→ \( y = \frac{2}{3}x + 4 \)
✔ Final Answer (slope-intercept form):
> \( \boxed{y = \frac{2}{3}x + 4} \)
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✔ Problem 4: Point (-8, -1); slope = \( -\frac{3}{4} \)
Step 1: Plug into point-slope formula
\( y - (-1) = -\frac{3}{4}(x - (-8)) \)
→ \( y + 1 = -\frac{3}{4}(x + 8) \)
Step 2: Distribute the slope
\( y + 1 = -\frac{3}{4}x - \frac{3}{4} \cdot 8 \)
→ \( y + 1 = -\frac{3}{4}x - 6 \)
Step 3: Solve for y (subtract 1 from both sides)
\( y = -\frac{3}{4}x - 6 - 1 \)
→ \( y = -\frac{3}{4}x - 7 \)
✔ Final Answer (slope-intercept form):
> \( \boxed{y = -\frac{3}{4}x - 7} \)
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📝 Summary of Answers:
3. \( \boxed{y = \frac{2}{3}x + 4} \)
4. \( \boxed{y = -\frac{3}{4}x - 7} \)
These are now in
slope-intercept form, as required!
Let me know if you want to check your work or need help with more problems!
Parent Tip: Review the logic above to help your child master the concept of writing linear equations worksheet answers.
