It looks like you've uploaded a worksheet titled
"Point-Slope Form Matching", which asks students to match the correct
point-slope form and
slope-intercept form of a line given a
slope (m) and a
point (x₁, y₁).
Let’s go through each row step by step and solve it. The goal is to:
1. Write the
point-slope form:
$$
y - y_1 = m(x - x_1)
$$
2. Convert that to
slope-intercept form:
$$
y = mx + b
$$
We are given:
- Slope $ m = 2 $
- Various points $ (x_1, y_1) $
---
Row 1: $ m = 2 $, Point $ (1, 3) $
Point-Slope Form:
$$
y - 3 = 2(x - 1)
$$
Slope-Intercept Form:
Start with point-slope:
$$
y - 3 = 2(x - 1)
\Rightarrow y - 3 = 2x - 2
\Rightarrow y = 2x + 1
$$
✔ So:
- Point-Slope: $ y - 3 = 2(x - 1) $
- Slope-Intercept: $ y = 2x + 1 $
---
Row 2: $ m = 2 $, Point $ (-3, 1) $
Point-Slope Form:
$$
y - 1 = 2(x + 3) \quad \text{(since } x - (-3) = x + 3\text{)}
$$
Slope-Intercept Form:
$$
y - 1 = 2x + 6
\Rightarrow y = 2x + 7
$$
✔ So:
- Point-Slope: $ y - 1 = 2(x + 3) $
- Slope-Intercept: $ y = 2x + 7 $
---
Row 3: $ m = 2 $, Point $ (-1, -3) $
Point-Slope Form:
$$
y + 3 = 2(x + 1)
$$
Slope-Intercept Form:
$$
y + 3 = 2x + 2
\Rightarrow y = 2x - 1
$$
✔ So:
- Point-Slope: $ y + 3 = 2(x + 1) $
- Slope-Intercept: $ y = 2x - 1 $
---
Row 4: $ m = 2 $, Point $ (1, -3) $
Point-Slope Form:
$$
y + 3 = 2(x - 1)
$$
Slope-Intercept Form:
$$
y + 3 = 2x - 2
\Rightarrow y = 2x - 5
$$
✔ So:
- Point-Slope: $ y + 3 = 2(x - 1) $
- Slope-Intercept: $ y = 2x - 5 $
---
Row 5: $ m = 2 $, Point $ (-3, -1) $
Point-Slope Form:
$$
y + 1 = 2(x + 3)
$$
Slope-Intercept Form:
$$
y + 1 = 2x + 6
\Rightarrow y = 2x + 5
$$
✔ So:
- Point-Slope: $ y + 1 = 2(x + 3) $
- Slope-Intercept: $ y = 2x + 5 $
---
Final Answer Summary:
| Slope | Point (x₁, y₁) | Point-Slope Form | Slope-Intercept Form |
|-------|----------------|------------------|------------------------|
| 2 | (1, 3) | $ y - 3 = 2(x - 1) $ | $ y = 2x + 1 $ |
| 2 | (-3, 1) | $ y - 1 = 2(x + 3) $ | $ y = 2x + 7 $ |
| 2 | (-1, -3) | $ y + 3 = 2(x + 1) $ | $ y = 2x - 1 $ |
| 2 | (1, -3) | $ y + 3 = 2(x - 1) $ | $ y = 2x - 5 $ |
| 2 | (-3, -1) | $ y + 1 = 2(x + 3) $ | $ y = 2x + 5 $ |
---
Explanation:
- The
point-slope form uses the formula $ y - y_1 = m(x - x_1) $. Plug in the values.
- To get
slope-intercept form, distribute the slope and solve for $ y $.
- All lines have the same slope (2), so they are parallel, but different y-intercepts due to different points.
Let me know if you'd like this formatted as a printable answer sheet or need help filling in the blanks on the worksheet!
Parent Tip: Review the logic above to help your child master the concept of point slope form worksheet.
