Question

write an equation (y = mx + b) for the graph
bike ride
m = slope (rate) \frac{rise}{run}
b = y - intercept (initial value)
y =
what is the meaning of the equation?

Explanation:

Step1: Find the slope \(m\)

The formula for slope \(m=\frac{y_2 - y_1}{x_2 - x_1}\). We can use two points \((0,9)\) and \((28,0)\).
\(m=\frac{0 - 9}{28-0}=-\frac{9}{28}\)

Step2: Find the \(y\) - intercept \(b\)

The \(y\) - intercept \(b\) is the value of \(y\) when \(x = 0\). From the point \((0,9)\), \(b = 9\)

Step3: Write the equation \(y=mx + b\)

Substitute \(m=-\frac{9}{28}\) and \(b = 9\) into \(y=mx + b\). So \(y=-\frac{9}{28}x+9\)

Answer:

The equation of the line is \(y =-\frac{9}{28}x + 9\). The meaning of the equation: The \(y\) - intercept \(b = 9\) represents the initial distance (in miles) from the recreation center at time \(x = 0\) minutes. The slope \(m=-\frac{9}{28}\) represents the rate at which the distance from the recreation center is changing per minute. The negative slope indicates that the distance from the recreation center is decreasing as time \(x\) (in minutes) increases.