You’ve uploaded a worksheet titled
“Writing Linear Equations (Given Two Points)”. The goal is to write the equation of a line that passes through two given points, and express the final answer in
slope-intercept form:
>
y = mx + b
---
##
✔ Step-by-Step Method (as shown in your worksheet):
Step 1: Use the Slope Formula
Given two points:
>
(x₁, y₁) and
(x₂, y₂)
The slope
m is calculated as:
>
m = (y₂ - y₁) / (x₂ - x₁)
---
Step 2: Use the Point-Slope Formula
Once you have the slope
m, plug it into the point-slope formula using one of the points (usually the first one for simplicity):
>
y - y₁ = m(x - x₁)
---
Step 3: Solve for y to get Slope-Intercept Form
Rearrange the equation to isolate
y on one side → this gives you
y = mx + b
---
## 📌 Example 1: Points (-3, 7) and (1, -1)
Step 1: Find Slope
> m = (y₂ - y₁)/(x₂ - x₁) = (-1 - 7)/(1 - (-3)) = (-8)/(4) =
-2
Step 2: Point-Slope Form (using point (-3, 7))
> y - 7 = -2(x - (-3))
> y - 7 = -2(x + 3)
Step 3: Simplify to Slope-Intercept Form
> y - 7 = -2x - 6
> Add 7 to both sides:
>
y = -2x + 1
✔ Final Answer:
y = -2x + 1
---
## 📌 Example 2: Points (-6, -7) and (3, -4)
Step 1: Find Slope
> m = (-4 - (-7))/(3 - (-6)) = (3)/(9) =
1/3
Step 2: Point-Slope Form (using point (-6, -7))
> y - (-7) = (1/3)(x - (-6))
> y + 7 = (1/3)(x + 6)
Step 3: Simplify to Slope-Intercept Form
> y + 7 = (1/3)x + 2
> Subtract 7 from both sides:
>
y = (1/3)x - 5
✔ Final Answer:
y = (1/3)x - 5
---
## 🧠 Key Takeaways:
- Always double-check your slope calculation — signs matter!
- You can use either point in the point-slope formula; you’ll get the same final equation.
- Slope-intercept form means
y = mx + b — make sure your answer looks like that.
---
## ✍️ Your Worksheet Already Solved These Correctly!
Your handwritten work matches the correct solutions:
- Example 1:
y = -2x + 1 ✔️
- Example 2:
y = (1/3)x - 5 ✔️
Great job! If you’re practicing, try these next:
> 🔹 Write the equation for points (2, 5) and (4, 9)
> 🔹 Write the equation for points (0, -3) and (5, 2)
Let me know if you want to check those too! 😊
Parent Tip: Review the logic above to help your child master the concept of writing equations in slope intercept form given two points worksheet.
