Question

khloe reaches the end of a hiking trail and hikes back to her car at a constant rate. after 1 hour (h), she is 8 miles (mi) from her car. after 3 h, she is 2 mi from her car. her distance from her car in miles, y, is a function of the time it takes to hike to her car in hours, x. points on the graph: (1, 8) and (3, 2) substitute the values of x and y to find the rate of change. rate of change: (2 - \square)/(\square - \square)

Explanation:

Step1: Recall rate of change formula

The rate of change (slope) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by \(\frac{y_2 - y_1}{x_2 - x_1}\). Here, the two points are \((1, 8)\) (so \(x_1 = 1\), \(y_1 = 8\)) and \((3, 2)\) (so \(x_2 = 3\), \(y_2 = 2\)).

Step2: Substitute values into the formula

For the numerator (change in \(y\)): \(y_2 - y_1 = 2 - 8\). For the denominator (change in \(x\)): \(x_2 - x_1 = 3 - 1\). So the rate of change expression is \(\frac{2 - 8}{3 - 1}\).

Answer:

The numerator's blank is \(8\), the denominator's first blank is \(3\), and the second blank is \(1\) (so the expression is \(\frac{2 - 8}{3 - 1}\))