Question

question 1-7
a machine on a production line packages calculators at a steady rate. after 10 minutes, it has packaged 25 calculators, and after 30 minutes it has packaged 75 calculators.
complete the equation to model the number of calculators, y, the machine has packaged after x minutes.
y = square x + square

Explanation:

Step1: Find the slope (rate of change)

The two points are \((10, 25)\) and \((30, 75)\). The slope \(m\) is calculated as \(m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{75 - 25}{30 - 10}=\frac{50}{20}=2.5\) or \(\frac{5}{2}\).

Step2: Use point - slope form to find the equation

Using the point \((10, 25)\) and the slope \(m = 2.5\), the point - slope form is \(y - y_1=m(x - x_1)\).
Substitute \(y_1 = 25\), \(m = 2.5\) and \(x_1 = 10\):
\(y-25 = 2.5(x - 10)\)
Expand the right - hand side: \(y-25=2.5x-25\)
Add 25 to both sides: \(y = 2.5x+0\) (or \(y=\frac{5}{2}x + 0\))

Answer:

\(y=\boxed{2.5}x+\boxed{0}\) (or \(y=\boxed{\frac{5}{2}}x+\boxed{0}\))