Question

1. the njhs students are busy raising money for the special olympics of maryland! on the 5th day of fundraising, anna and marina had $200. on the 8th day of fundraising, they had raised $260 for the polar plunge. write a linear equation to model their fundraising efforts. (hint: make a table using (5,200) and (8, 260) to calculate the slope and work backward to find the y - intercept).

Explanation:

Step1: Calculate the slope (m)

The formula for slope between two points \((x_1, y_1)\) and \((x_2, y_2)\) is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Here, \((x_1, y_1)=(5, 200)\) and \((x_2, y_2)=(8, 260)\).
\[m=\frac{260 - 200}{8 - 5}=\frac{60}{3}=20\]

Step2: Use point - slope form to find the equation

The point - slope form of a linear equation is \(y - y_1=m(x - x_1)\). We can use the point \((5, 200)\) and \(m = 20\).
\[y-200 = 20(x - 5)\]
Expand the right - hand side:
\[y-200=20x-100\]
Add 200 to both sides of the equation:
\[y=20x + 100\]

Answer:

\(y = 20x+100\)