Graphing Slope Intercept Form ≡ Fill Out Printable PDF Forms Online - Free Printable

To solve the problem of graphing the lines given in slope-intercept form, we will follow these steps for each equation:

1. \( y = -8x - 4 \)

#### Step 1: Identify the slope and y-intercept
- The equation is in the slope-intercept form \( y = mx + b \), where:
- \( m \) (slope) = \(-8\)
- \( b \) (y-intercept) = \(-4\)

#### Step 2: Plot the y-intercept
- The y-intercept is \((0, -4)\). Plot this point on the graph.

#### Step 3: Use the slope to find another point
- The slope \( m = -8 \) means "rise over run" is \(-8/1\).
- From the y-intercept \((0, -4)\), move down 8 units and right 1 unit to get the next point.
- This gives the point \((1, -12)\).

#### Step 4: Draw the line
- Connect the points \((0, -4)\) and \((1, -12)\) with a straight line.

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

#### Step 1: Identify the slope and y-intercept
- The equation is in the slope-intercept form \( y = mx + b \), where:
- \( m \) (slope) = \(-1\)
- \( b \) (y-intercept) = \(5\)

#### Step 2: Plot the y-intercept
- The y-intercept is \((0, 5)\). Plot this point on the graph.

#### Step 3: Use the slope to find another point
- The slope \( m = -1 \) means "rise over run" is \(-1/1\).
- From the y-intercept \((0, 5)\), move down 1 unit and right 1 unit to get the next point.
- This gives the point \((1, 4)\).

#### Step 4: Draw the line
- Connect the points \((0, 5)\) and \((1, 4)\) with a straight line.

3. \( y = 2x \)

#### Step 1: Identify the slope and y-intercept
- The equation is in the slope-intercept form \( y = mx + b \), where:
- \( m \) (slope) = \(2\)
- \( b \) (y-intercept) = \(0\)

#### Step 2: Plot the y-intercept
- The y-intercept is \((0, 0)\). Plot this point on the graph.

#### Step 3: Use the slope to find another point
- The slope \( m = 2 \) means "rise over run" is \(2/1\).
- From the y-intercept \((0, 0)\), move up 2 units and right 1 unit to get the next point.
- This gives the point \((1, 2)\).

#### Step 4: Draw the line
- Connect the points \((0, 0)\) and \((1, 2)\) with a straight line.

4. \( x = -4 \)

#### Step 1: Understand the equation
- The equation \( x = -4 \) represents a vertical line where the x-coordinate is always \(-4\).

#### Step 2: Plot points on the vertical line
- Choose any y-values and keep \( x = -4 \):
- Points could be \((-4, 0)\), \((-4, 2)\), \((-4, -2)\), etc.

#### Step 3: Draw the vertical line
- Draw a vertical line passing through all points where \( x = -4 \).

Final Answer

The graphs for each equation are as follows:

1. \( y = -8x - 4 \): A line with a steep negative slope passing through \((0, -4)\) and \((1, -12)\).
2. \( y = -x + 5 \): A line with a negative slope passing through \((0, 5)\) and \((1, 4)\).
3. \( y = 2x \): A line with a positive slope passing through \((0, 0)\) and \((1, 2)\).
4. \( x = -4 \): A vertical line at \( x = -4 \).

\[
\boxed{\text{Graphs as described above}}
\]