Question

x: number of minutes
y: number of steps
what does the equation y = 15x + 30 tell you?
hassan starts at the ? and climbs up ? steps each minute.
(chart: hassan: y = 15x + 30, jenny: y = 15x, x-axis: minutes (0 - 9), y-axis: steps (0 - 135))

Explanation:

Step1: Analyze the y - intercept

The equation of a line is in the form \(y = mx + b\), where \(b\) is the y - intercept (the value of \(y\) when \(x = 0\)) and \(m\) is the slope (the rate of change). For the equation \(y=15x + 30\), when \(x = 0\) (0 minutes), \(y=15\times0+30=30\). So the y - intercept is 30, which means Hassan starts at 30 steps.

Step2: Analyze the slope

The coefficient of \(x\) in the equation \(y = mx + b\) is the slope. In the equation \(y = 15x+30\), the coefficient of \(x\) is 15. The slope represents the rate of change, which in this context (where \(x\) is minutes and \(y\) is steps) means the number of steps climbed per minute. So Hassan climbs up 15 steps each minute.

Answer:

Hassan starts at the 30 steps and climbs up 15 steps each minute.