Samantha is raising money for a local charity. She is required to raise at least $500.00 through corporate and individual sponsorships. Each corporate sponsorship raises $100.00, and each individual sponsorship raises $25.00.

Which graph represents the situation?

3 answers

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:

  1. Shows the line \( 4x + y = 20 \).
  2. Shades the region above this line, including the line itself.
  3. 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.

is the line dashed or not

In this case, the line should be solid, not dashed.

Since the inequality is \(4x + y \geq 20\), the solid line indicates that points on the line itself (where \(4x + y = 20\)) are included in the solution set. This means combinations of corporate and individual sponsorships that yield exactly $500 are valid, along with those combinations that yield more than $500, which is represented by the shaded region above the line.

So, to summarize:

  • The line \(4x + y = 20\) should be solid.
  • The area above the line (where \(4x + y > 20\)) should be shaded.