To represent Samantha’s fundraising situation with a graph, we can use a coordinate plane where one axis represents the number of corporate sponsorships (let's say this is the x-axis) and the other axis represents the number of individual sponsorships (let's say this is the y-axis).
Step 1: Set Up the Equation
The total amount raised from corporate and individual sponsorships can be expressed with the following equation:
\[ 100x + 25y \geq 500 \]
Where:
- \( x \) = Number of corporate sponsorships
- \( y \) = Number of individual sponsorships
Step 2: Simplify the Equation
We can simplify this inequality. First, we can divide the entire inequality by 25:
\[ 4x + y \geq 20 \]
Step 3: Identify the Line
The line that represents the equation \( 4x + y = 20 \) can be determined by finding intercepts:
- If \( x = 0 \), then \( y = 20 \) (y-intercept).
- If \( y = 0 \), then \( 4x = 20 \), which gives \( x = 5 \) (x-intercept).
Step 4: Graph the Line
You can plot the points \((0, 20)\) and \((5, 0)\) on a graph, and then draw the line passing through these points. Since the inequality is \( \geq \), you will shade the area above (including the line) which represents all the combinations of corporate and individual sponsorships that meet or exceed the target of $500.
Step 5: Axes Limits
Since both \( x \) and \( y \) must be non-negative, you will restrict your graph to the first quadrant.
Final Graph
You will look for a graph that:
- Shows the line \( 4x + y = 20 \).
- Shades the region above this line, including the line itself.
- Contains only points in the first quadrant where both \( x \) and \( y \) are non-negative.
This is the graph that represents Samantha's fundraising situation.