Question

what is the slope of this line?

Explanation:

Step1: Identify two points on the line

From the graph, we can see that the line passes through \((0, 0)\) (the origin) and \((4, 16)\) (we can also use other points, but these are easy to identify).

Step2: Use the slope formula

The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Let \((x_1,y_1)=(0,0)\) and \((x_2,y_2)=(4,16)\). Then \(m = \frac{16 - 0}{4 - 0}=\frac{16}{4}=4\). We can also check with another pair of points, say \((0,0)\) and \((2,8)\), then \(m=\frac{8 - 0}{2 - 0}=\frac{8}{2} = 4\), or \((0,0)\) and \((1,4)\), \(m=\frac{4-0}{1 - 0}=4\). So the slope is consistent.

Answer:

The slope of the line is \(4\).