Let's solve the problems on this worksheet step by step.
---
Problem 1:
Equation: $ 3x - 2y = 12 $
We are asked to find:
- The
x-intercept
- The
y-intercept
- Then plot both points and draw a line through them.
---
####
Step 1: Find the x-intercept
The
x-intercept occurs when $ y = 0 $.
Substitute $ y = 0 $ into the equation:
$$
3x - 2(0) = 12 \\
3x = 12 \\
x = \frac{12}{3} = 4
$$
✔ So, the
x-intercept is (4, 0).
---
####
Step 2: Find the y-intercept
The
y-intercept occurs when $ x = 0 $.
Substitute $ x = 0 $ into the equation:
$$
3(0) - 2y = 12 \\
-2y = 12 \\
y = \frac{12}{-2} = -6
$$
✔ So, the
y-intercept is (0, -6).
---
####
Step 3: Plotting and Graphing
On the coordinate plane:
- Plot the point $ (4, 0) $
- Plot the point $ (0, -6) $
- Draw a straight line through these two points.
This line represents the graph of $ 3x - 2y = 12 $.
---
✔ Answer for Problem 1:
-
x-intercept: $ (4, 0) $
-
y-intercept: $ (0, -6) $
---
Problem 2:
Equation: $ 4x + 2y = 14 $
Again, find:
- x-intercept
- y-intercept
- Graph the line
---
####
Step 1: Find the x-intercept
Set $ y = 0 $:
$$
4x + 2(0) = 14 \\
4x = 14 \\
x = \frac{14}{4} = \frac{7}{2} = 3.5
$$
✔ So, the
x-intercept is (3.5, 0) or $ \left(\frac{7}{2}, 0\right) $
---
####
Step 2: Find the y-intercept
Set $ x = 0 $:
$$
4(0) + 2y = 14 \\
2y = 14 \\
y = \frac{14}{2} = 7
$$
✔ So, the
y-intercept is (0, 7)
---
####
Step 3: Plotting and Graphing
- Plot $ (3.5, 0) $
- Plot $ (0, 7) $
- Draw a straight line through them.
---
✔ Answer for Problem 2:
-
x-intercept: $ (3.5, 0) $ or $ \left(\frac{7}{2}, 0\right) $
-
y-intercept: $ (0, 7) $
---
✔ Summary:
| Problem | Equation | x-intercept | y-intercept |
|--------|------------------|-------------------|------------------|
| 1 | $ 3x - 2y = 12 $ | $ (4, 0) $ | $ (0, -6) $ |
| 2 | $ 4x + 2y = 14 $ | $ (3.5, 0) $ | $ (0, 7) $ |
> 📌
Tip: To avoid fractions, you can multiply the entire equation by 2 in problem 2 to eliminate decimals if needed, but it's not necessary here.
---
Now, go ahead and plot these points on the graphs provided in your worksheet. You’ll get two straight lines — one going from (4,0) to (0,-6), and the other from (3.5,0) to (0,7). That’s how you graph linear equations using intercepts!
Parent Tip: Review the logic above to help your child master the concept of linear equations graphing worksheet.
