Question

1. find the slope of the line.

slope = \frac{rise}{run}
= \frac{\square}{\square}, or \square
the slope is \square.
chart: x-axis labeled time (min) from 0 to 10, y-axis labeled items from 0 to 50, line passing through (0,0) and (10,50) (approximate, based on grid)

Explanation:

Step1: Identify two points on the line

The line passes through the origin \((0, 0)\) and another point, for example, when \(x = 10\), \(y = 50\) (from the graph, we can also check other points like when \(x = 5\), \(y = 25\) etc.). Let's take \((0, 0)\) and \((10, 50)\).

Step2: Calculate rise and run

Rise is the change in \(y\), so \(50 - 0 = 50\). Run is the change in \(x\), so \(10 - 0 = 10\).

Step3: Compute the slope

Slope \(=\frac{\text{rise}}{\text{run}}=\frac{50}{10} = 5\). We can also check with another pair, say \((0,0)\) and \((5,25)\): rise \(= 25 - 0 = 25\), run \(= 5 - 0 = 5\), slope \(=\frac{25}{5}=5\).

Answer:

The slope is \(\frac{50}{10}\) (or \(\frac{25}{5}\) etc.), and the simplified slope is \(5\). So filling in the boxes: slope \(=\frac{\boldsymbol{50}}{\boldsymbol{10}}\), or \(\boldsymbol{5}\). The slope is \(\boldsymbol{5}\).