Of course! I'll solve each of the six linear equations by finding their
x-intercept and
y-intercept, then explain how to graph them. Since I can't see the image, I'm working from the text you provided.
---
📌 Key Concept:
To find the
x-intercept, set
y = 0 and solve for
x.
To find the
y-intercept, set
x = 0 and solve for
y.
Once you have both intercepts, plot them on the coordinate plane and draw a straight line through them.
---
## 🔢 Problem 1: `x + 3y = 8`
-
x-intercept: Set y = 0
→ x + 3(0) = 8 →
x = 8
→ Point:
(8, 0)
-
y-intercept: Set x = 0
→ 0 + 3y = 8 → y = 8/3 ≈
2.67
→ Point:
(0, 8/3)
✔ Answer:
x-int =
8
y-int =
8/3
---
## 🔢 Problem 2: `3x - y = 9`
-
x-intercept: Set y = 0
→ 3x - 0 = 9 → x = 9/3 =
3
→ Point:
(3, 0)
-
y-intercept: Set x = 0
→ 3(0) - y = 9 → -y = 9 →
y = -9
→ Point:
(0, -9)
✔ Answer:
x-int =
3
y-int =
-9
---
## 🔢 Problem 3: `-5x + 4y = 20`
-
x-intercept: Set y = 0
→ -5x + 0 = 20 → x = 20 / (-5) =
-4
→ Point:
(-4, 0)
-
y-intercept: Set x = 0
→ 0 + 4y = 20 → y = 20/4 =
5
→ Point:
(0, 5)
✔ Answer:
x-int =
-4
y-int =
5
---
## 🔢 Problem 4: `4x + 3y = -9`
-
x-intercept: Set y = 0
→ 4x + 0 = -9 → x = -9/4 =
-2.25
→ Point:
(-9/4, 0)
-
y-intercept: Set x = 0
→ 0 + 3y = -9 → y = -9/3 =
-3
→ Point:
(0, -3)
✔ Answer:
x-int =
-9/4
y-int =
-3
---
## 🔢 Problem 5: `-3x + y = 6`
-
x-intercept: Set y = 0
→ -3x + 0 = 6 → x = 6 / (-3) =
-2
→ Point:
(-2, 0)
-
y-intercept: Set x = 0
→ 0 + y = 6 →
y = 6
→ Point:
(0, 6)
✔ Answer:
x-int =
-2
y-int =
6
---
## 🔢 Problem 6: `5x - 3y = 15`
-
x-intercept: Set y = 0
→ 5x - 0 = 15 → x = 15/5 =
3
→ Point:
(3, 0)
-
y-intercept: Set x = 0
→ 0 - 3y = 15 → -3y = 15 → y =
-5
→ Point:
(0, -5)
✔ Answer:
x-int =
3
y-int =
-5
---
## 📈 How to Graph Each Line:
For each problem:
1. On the grid, locate the
x-intercept (on the x-axis).
2. Locate the
y-intercept (on the y-axis).
3. Draw a straight line connecting these two points.
4. Extend the line in both directions with arrows (since lines go infinitely).
> 💡 Tip: If an intercept is a fraction (like 8/3 or -9/4), estimate its position on the grid — for example, 8/3 is between 2 and 3, closer to 3.
---
##
✔ Final Answers Summary:
| Problem | Equation | x-intercept | y-intercept |
|---------|------------------|-------------|-------------|
| 1 | x + 3y = 8 | 8 | 8/3 |
| 2 | 3x - y = 9 | 3 | -9 |
| 3 | -5x + 4y = 20 | -4 | 5 |
| 4 | 4x + 3y = -9 | -9/4 | -3 |
| 5 | -3x + y = 6 | -2 | 6 |
| 6 | 5x - 3y = 15 | 3 | -5 |
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Let me know if you’d like me to describe how to plot any of these on a specific grid or help you check your graphs! 😊
Parent Tip: Review the logic above to help your child master the concept of linear equations standard form worksheet.
