Standard Form Linear Equation Worksheet - Fill Online, Printable ... - Free Printable

Since I can't view or access images directly, I can't see the specific equations or graphs in your uploaded image. However, based on the text you've provided, it looks like you're working on a worksheet where you need to:

1. Find the x- and y-intercepts of each linear equation.
2. Graph the line using those intercepts.

Let me walk through how to solve each problem step-by-step, assuming the equations are as listed:

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General Method: Finding Intercepts

To find:
- x-intercept: Set $ y = 0 $ and solve for $ x $.
- y-intercept: Set $ x = 0 $ and solve for $ y $.

Then plot these two points and draw a line through them.

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Let’s go through each equation one by one.

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1) $ x + 2y = 8 $

#### x-intercept (set $ y = 0 $):
$$
x + 2(0) = 8 \Rightarrow x = 8
\Rightarrow \text{x-int} = (8, 0)
$$

#### y-intercept (set $ x = 0 $):
$$
0 + 2y = 8 \Rightarrow y = 4
\Rightarrow \text{y-int} = (0, 4)
$$

✔ So:
- x-int = 8
- y-int = 4

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2) $ 3x - y = 9 $

#### x-intercept (set $ y = 0 $):
$$
3x - 0 = 9 \Rightarrow x = 3
\Rightarrow \text{x-int} = (3, 0)
$$

#### y-intercept (set $ x = 0 $):
$$
0 - y = 9 \Rightarrow y = -9
\Rightarrow \text{y-int} = (0, -9)
$$

✔ So:
- x-int = 3
- y-int = -9

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3) $ 5x + 3y = 30 $

#### x-intercept ($ y = 0 $):
$$
5x + 0 = 30 \Rightarrow x = 6
\Rightarrow \text{x-int} = (6, 0)
$$

#### y-intercept ($ x = 0 $):
$$
0 + 3y = 30 \Rightarrow y = 10
\Rightarrow \text{y-int} = (0, 10)
$$

✔ So:
- x-int = 6
- y-int = 10

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4) $ 4x + 2y = -8 $

#### x-intercept ($ y = 0 $):
$$
4x + 0 = -8 \Rightarrow x = -2
\Rightarrow \text{x-int} = (-2, 0)
$$

#### y-intercept ($ x = 0 $):
$$
0 + 2y = -8 \Rightarrow y = -4
\Rightarrow \text{y-int} = (0, -4)
$$

✔ So:
- x-int = -2
- y-int = -4

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5) $ 3x + y = 4 $

#### x-intercept ($ y = 0 $):
$$
3x + 0 = 4 \Rightarrow x = \frac{4}{3}
\Rightarrow \text{x-int} = \left(\frac{4}{3}, 0\right)
$$

#### y-intercept ($ x = 0 $):
$$
0 + y = 4 \Rightarrow y = 4
\Rightarrow \text{y-int} = (0, 4)
$$

✔ So:
- x-int = $ \frac{4}{3} $ (or approximately 1.33)
- y-int = 4

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6) $ 5x - 3y = 15 $

#### x-intercept ($ y = 0 $):
$$
5x - 0 = 15 \Rightarrow x = 3
\Rightarrow \text{x-int} = (3, 0)
$$

#### y-intercept ($ x = 0 $):
$$
0 - 3y = 15 \Rightarrow y = -5
\Rightarrow \text{y-int} = (0, -5)
$$

✔ So:
- x-int = 3
- y-int = -5

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✔ Summary Table:

| Problem | Equation | x-intercept | y-intercept |
|--------|------------------|-------------|-------------|
| 1 | $ x + 2y = 8 $ | 8 | 4 |
| 2 | $ 3x - y = 9 $ | 3 | -9 |
| 3 | $ 5x + 3y = 30 $ | 6 | 10 |
| 4 | $ 4x + 2y = -8 $ | -2 | -4 |
| 5 | $ 3x + y = 4 $ | $ \frac{4}{3} $ | 4 |
| 6 | $ 5x - 3y = 15 $ | 3 | -5 |

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🔧 How to Graph:

For each equation:
1. Plot the x-intercept on the x-axis.
2. Plot the y-intercept on the y-axis.
3. Draw a straight line through both points.

> Example: For #1: Plot (8, 0) and (0, 4), then draw the line.

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If you'd like, you can now fill in the blanks on your worksheet with the values above.

Let me know if you want help sketching any of the graphs or converting to slope-intercept form!