Graphing Linear Equation Worksheets - Free Printable

To solve the problem of graphing lines given in slope-intercept form, we need to follow these steps:

Step 1: Understand the Slope-Intercept Form

The equation of a line in slope-intercept form is:
\[
y = mx + b
\]
where:
- \( m \) is the slope of the line.
- \( b \) is the y-intercept (the point where the line crosses the y-axis).

Step 2: Identify the Slope and Y-Intercept

For each equation, identify the values of \( m \) (slope) and \( b \) (y-intercept).

Step 3: Plot the Y-Intercept

The y-intercept \( b \) is the point where the line crosses the y-axis. This point is always \((0, b)\). Plot this point on the graph.

Step 4: Use the Slope to Find Another Point

The slope \( m \) is given as a fraction \( \frac{\text{rise}}{\text{run}} \):
- Rise: How many units to move up (positive) or down (negative).
- Run: How many units to move right (positive).

Starting from the y-intercept, use the slope to find another point on the line.

Step 5: Draw the Line

Connect the y-intercept and the second point with a straight line. Extend the line in both directions if necessary.

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Let's Solve Each Equation

#### (a) \( y = -x + 4 \)
1. Identify \( m \) and \( b \):
- Slope \( m = -1 \) (or \(\frac{-1}{1}\))
- Y-intercept \( b = 4 \)

2. Plot the Y-Intercept:
- The y-intercept is \((0, 4)\).

3. Use the Slope:
- Slope \( m = -1 \): Move down 1 unit and right 1 unit from \((0, 4)\).
- New point: \((1, 3)\).

4. Draw the Line:
- Connect \((0, 4)\) and \((1, 3)\).

#### (b) \( y = x + 2 \)
1. Identify \( m \) and \( b \):
- Slope \( m = 1 \) (or \(\frac{1}{1}\))
- Y-intercept \( b = 2 \)

2. Plot the Y-Intercept:
- The y-intercept is \((0, 2)\).

3. Use the Slope:
- Slope \( m = 1 \): Move up 1 unit and right 1 unit from \((0, 2)\).
- New point: \((1, 3)\).

4. Draw the Line:
- Connect \((0, 2)\) and \((1, 3)\).

#### (c) \( y = -2x + 1 \)
1. Identify \( m \) and \( b \):
- Slope \( m = -2 \) (or \(\frac{-2}{1}\))
- Y-intercept \( b = 1 \)

2. Plot the Y-Intercept:
- The y-intercept is \((0, 1)\).

3. Use the Slope:
- Slope \( m = -2 \): Move down 2 units and right 1 unit from \((0, 1)\).
- New point: \((1, -1)\).

4. Draw the Line:
- Connect \((0, 1)\) and \((1, -1)\).

#### (d) \( y = 2x - 3 \)
1. Identify \( m \) and \( b \):
- Slope \( m = 2 \) (or \(\frac{2}{1}\))
- Y-intercept \( b = -3 \)

2. Plot the Y-Intercept:
- The y-intercept is \((0, -3)\).

3. Use the Slope:
- Slope \( m = 2 \): Move up 2 units and right 1 unit from \((0, -3)\).
- New point: \((1, -1)\).

4. Draw the Line:
- Connect \((0, -3)\) and \((1, -1)\).

#### (e) \( y = -\frac{1}{2}x + 3 \)
1. Identify \( m \) and \( b \):
- Slope \( m = -\frac{1}{2} \)
- Y-intercept \( b = 3 \)

2. Plot the Y-Intercept:
- The y-intercept is \((0, 3)\).

3. Use the Slope:
- Slope \( m = -\frac{1}{2} \): Move down 1 unit and right 2 units from \((0, 3)\).
- New point: \((2, 2)\).

4. Draw the Line:
- Connect \((0, 3)\) and \((2, 2)\).

#### (f) \( 2y = x \)
1. Rewrite in slope-intercept form:
\[
y = \frac{1}{2}x
\]
- Slope \( m = \frac{1}{2} \)
- Y-intercept \( b = 0 \)

2. Plot the Y-Intercept:
- The y-intercept is \((0, 0)\).

3. Use the Slope:
- Slope \( m = \frac{1}{2} \): Move up 1 unit and right 2 units from \((0, 0)\).
- New point: \((2, 1)\).

4. Draw the Line:
- Connect \((0, 0)\) and \((2, 1)\).

#### (g) \( 3y = -x + 6 \)
1. Rewrite in slope-intercept form:
\[
y = -\frac{1}{3}x + 2
\]
- Slope \( m = -\frac{1}{3} \)
- Y-intercept \( b = 2 \)

2. Plot the Y-Intercept:
- The y-intercept is \((0, 2)\).

3. Use the Slope:
- Slope \( m = -\frac{1}{3} \): Move down 1 unit and right 3 units from \((0, 2)\).
- New point: \((3, 1)\).

4. Draw the Line:
- Connect \((0, 2)\) and \((3, 1)\).

#### (h) \( 2y = 3x - 6 \)
1. Rewrite in slope-intercept form:
\[
y = \frac{3}{2}x - 3
\]
- Slope \( m = \frac{3}{2} \)
- Y-intercept \( b = -3 \)

2. Plot the Y-Intercept:
- The y-intercept is \((0, -3)\).

3. Use the Slope:
- Slope \( m = \frac{3}{2} \): Move up 3 units and right 2 units from \((0, -3)\).
- New point: \((2, 0)\).

4. Draw the Line:
- Connect \((0, -3)\) and \((2, 0)\).

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Final Answer

Graph each line by following the steps above. The final graphs will show the lines corresponding to each equation.

\[
\boxed{\text{Graph each line using the steps outlined.}}
\]