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

To solve the problem, we need to find the x-intercepts and y-intercepts of each linear equation and then graph the lines. Let's go through each equation step by step.

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1) \( x + 2y = 8 \)

#### Finding the x-intercept:
- Set \( y = 0 \):
\[
x + 2(0) = 8 \implies x = 8
\]
- The x-intercept is \( (8, 0) \).

#### Finding the y-intercept:
- Set \( x = 0 \):
\[
0 + 2y = 8 \implies y = 4
\]
- The y-intercept is \( (0, 4) \).

#### Graphing:
- Plot the points \( (8, 0) \) and \( (0, 4) \).
- Draw a straight line through these points.

---

2) \( 3x - y = 9 \)

#### Finding the x-intercept:
- Set \( y = 0 \):
\[
3x - 0 = 9 \implies x = 3
\]
- The x-intercept is \( (3, 0) \).

#### Finding the y-intercept:
- Set \( x = 0 \):
\[
3(0) - y = 9 \implies y = -9
\]
- The y-intercept is \( (0, -9) \).

#### Graphing:
- Plot the points \( (3, 0) \) and \( (0, -9) \).
- Draw a straight line through these points.

---

3) \( 5x + 6y = 30 \)

#### Finding the x-intercept:
- Set \( y = 0 \):
\[
5x + 6(0) = 30 \implies x = 6
\]
- The x-intercept is \( (6, 0) \).

#### Finding the y-intercept:
- Set \( x = 0 \):
\[
5(0) + 6y = 30 \implies y = 5
\]
- The y-intercept is \( (0, 5) \).

#### Graphing:
- Plot the points \( (6, 0) \) and \( (0, 5) \).
- Draw a straight line through these points.

---

4) \( 4x + 3y = -9 \)

#### Finding the x-intercept:
- Set \( y = 0 \):
\[
4x + 3(0) = -9 \implies x = -\frac{9}{4}
\]
- The x-intercept is \( \left( -\frac{9}{4}, 0 \right) \).

#### Finding the y-intercept:
- Set \( x = 0 \):
\[
4(0) + 3y = -9 \implies y = -3
\]
- The y-intercept is \( (0, -3) \).

#### Graphing:
- Plot the points \( \left( -\frac{9}{4}, 0 \right) \) and \( (0, -3) \).
- Draw a straight line through these points.

---

5) \( 4x + y = 6 \)

#### Finding the x-intercept:
- Set \( y = 0 \):
\[
4x + 0 = 6 \implies x = \frac{6}{4} = \frac{3}{2}
\]
- The x-intercept is \( \left( \frac{3}{2}, 0 \right) \).

#### Finding the y-intercept:
- Set \( x = 0 \):
\[
4(0) + y = 6 \implies y = 6
\]
- The y-intercept is \( (0, 6) \).

#### Graphing:
- Plot the points \( \left( \frac{3}{2}, 0 \right) \) and \( (0, 6) \).
- Draw a straight line through these points.

---

6) \( 5x - 3y = 15 \)

#### Finding the x-intercept:
- Set \( y = 0 \):
\[
5x - 3(0) = 15 \implies x = 3
\]
- The x-intercept is \( (3, 0) \).

#### Finding the y-intercept:
- Set \( x = 0 \):
\[
5(0) - 3y = 15 \implies y = -5
\]
- The y-intercept is \( (0, -5) \).

#### Graphing:
- Plot the points \( (3, 0) \) and \( (0, -5) \).
- Draw a straight line through these points.

---

Final Answer:

The intercepts for each equation are as follows:

1. \( x + 2y = 8 \):
- x-intercept: \( (8, 0) \)
- y-intercept: \( (0, 4) \)

2. \( 3x - y = 9 \):
- x-intercept: \( (3, 0) \)
- y-intercept: \( (0, -9) \)

3. \( 5x + 6y = 30 \):
- x-intercept: \( (6, 0) \)
- y-intercept: \( (0, 5) \)

4. \( 4x + 3y = -9 \):
- x-intercept: \( \left( -\frac{9}{4}, 0 \right) \)
- y-intercept: \( (0, -3) \)

5. \( 4x + y = 6 \):
- x-intercept: \( \left( \frac{3}{2}, 0 \right) \)
- y-intercept: \( (0, 6) \)

6. \( 5x - 3y = 15 \):
- x-intercept: \( (3, 0) \)
- y-intercept: \( (0, -5) \)

\[
\boxed{
\begin{array}{ll}
1) & \text{x-intercept: } (8, 0), \text{ y-intercept: } (0, 4) \\
2) & \text{x-intercept: } (3, 0), \text{ y-intercept: } (0, -9) \\
3) & \text{x-intercept: } (6, 0), \text{ y-intercept: } (0, 5) \\
4) & \text{x-intercept: } \left( -\frac{9}{4}, 0 \right), \text{ y-intercept: } (0, -3) \\
5) & \text{x-intercept: } \left( \frac{3}{2}, 0 \right), \text{ y-intercept: } (0, 6) \\
6) & \text{x-intercept: } (3, 0), \text{ y-intercept: } (0, -5) \\
\end{array}
}
\]

For each equation, graph the line using the intercepts.