Question

what is the slope of this line? (with a coordinate grid and a blue line plotted)

Explanation:

Step1: Identify two points on the line

We can see that the line passes through \((0, 4)\) and \((2, 8)\) (we can choose other points too, but these are easy to identify). Let \((x_1, y_1)=(0, 4)\) and \((x_2, y_2)=(2, 8)\).

Step2: Use 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 \(m = \frac{y_2 - y_1}{x_2 - x_1}\).

Substituting the values: \(m=\frac{8 - 4}{2 - 0}=\frac{4}{2} = 2\).

We can also check with another pair of points, say \((0, 4)\) and \((-2, 0)\). Then \(m=\frac{0 - 4}{-2 - 0}=\frac{-4}{-2}=2\).

Answer:

The slope of the line is \(2\).