Question

rohan is the manager at a restaurant. the graph shows the relationship between the number of hours he works, x, and the amount of money he makes, y. what is the slope of the line?

Explanation:

Step1: Recall the slope formula

The slope \( m \) of a line passing through two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by \( m=\frac{y_2 - y_1}{x_2 - x_1} \). Since the line passes through the origin \((0,0)\), we can choose another point on the line. Let's pick the point \((10, 240)\) (from the graph, when \( x = 10 \), \( y = 240 \)).

Step2: Calculate the slope

Using the points \((0,0)\) and \((10, 240)\), substitute into the slope formula: \( m=\frac{240 - 0}{10 - 0}=\frac{240}{10} = 24 \). We can also check with another point, say \((5, 120)\): \( m=\frac{120 - 0}{5 - 0}=\frac{120}{5}=24 \), which confirms the slope.

Answer:

24