Graphing Lines Using Standard Form worksheets - Free Printable

To solve the problem of graphing each line using the standard form equations, we will follow these steps for each equation:

1. Rewrite the equation in slope-intercept form (if necessary) to easily identify the slope and y-intercept.
2. Identify key points (such as the x-intercept and y-intercept) or use the slope and y-intercept to plot the line.
3. Plot the points on the graph and draw the line.

Let's go through each equation step by step.

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1. \( 3x + 5y = 15 \)

#### Step 1: Find the intercepts
- y-intercept: Set \( x = 0 \):
\[
3(0) + 5y = 15 \implies 5y = 15 \implies y = 3
\]
So, the y-intercept is \( (0, 3) \).

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

#### Step 2: Plot the points and draw the line
- Plot \( (0, 3) \) and \( (5, 0) \).
- Draw a straight line through these points.

---

2. \( -2x + 3y = -6 \)

#### Step 1: Find the intercepts
- y-intercept: Set \( x = 0 \):
\[
-2(0) + 3y = -6 \implies 3y = -6 \implies y = -2
\]
So, the y-intercept is \( (0, -2) \).

- x-intercept: Set \( y = 0 \):
\[
-2x + 3(0) = -6 \implies -2x = -6 \implies x = 3
\]
So, the x-intercept is \( (3, 0) \).

#### Step 2: Plot the points and draw the line
- Plot \( (0, -2) \) and \( (3, 0) \).
- Draw a straight line through these points.

---

3. \( 2x + y = 4 \)

#### Step 1: Find the intercepts
- y-intercept: Set \( x = 0 \):
\[
2(0) + y = 4 \implies y = 4
\]
So, the y-intercept is \( (0, 4) \).

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

#### Step 2: Plot the points and draw the line
- Plot \( (0, 4) \) and \( (2, 0) \).
- Draw a straight line through these points.

---

4. \( x - 4y = 4 \)

#### Step 1: Find the intercepts
- y-intercept: Set \( x = 0 \):
\[
0 - 4y = 4 \implies -4y = 4 \implies y = -1
\]
So, the y-intercept is \( (0, -1) \).

- x-intercept: Set \( y = 0 \):
\[
x - 4(0) = 4 \implies x = 4
\]
So, the x-intercept is \( (4, 0) \).

#### Step 2: Plot the points and draw the line
- Plot \( (0, -1) \) and \( (4, 0) \).
- Draw a straight line through these points.

---

5. \( x + 2y = 4 \)

#### Step 1: Find the intercepts
- y-intercept: Set \( x = 0 \):
\[
0 + 2y = 4 \implies 2y = 4 \implies y = 2
\]
So, the y-intercept is \( (0, 2) \).

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

#### Step 2: Plot the points and draw the line
- Plot \( (0, 2) \) and \( (4, 0) \).
- Draw a straight line through these points.

---

6. \( -2y - 5x = 10 \)

#### Step 1: Find the intercepts
- y-intercept: Set \( x = 0 \):
\[
-2y - 5(0) = 10 \implies -2y = 10 \implies y = -5
\]
So, the y-intercept is \( (0, -5) \).

- x-intercept: Set \( y = 0 \):
\[
-2(0) - 5x = 10 \implies -5x = 10 \implies x = -2
\]
So, the x-intercept is \( (-2, 0) \).

#### Step 2: Plot the points and draw the line
- Plot \( (0, -5) \) and \( (-2, 0) \).
- Draw a straight line through these points.

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Final Answer

The graphs of the lines are sketched by plotting the intercepts and drawing a straight line through them. The final answer is:

\[
\boxed{\text{Graphs are sketched as described above.}}
\]