Question

what is the slope of the line graphed in the given coordinate plane?

Explanation:

Step1: Identify two points on the line

The line passes through the origin \((0,0)\) and another point, for example, \((10, -2)\) (by observing the graph, when \(x = 10\), \(y=- 2\)).

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 \((x_2,y_2)=(10, - 2)\). Then \(m=\frac{-2 - 0}{10 - 0}=\frac{-2}{10}=-\frac{1}{5}\). We can also check with another point, say \((5, - 1)\). Using \((0,0)\) and \((5, - 1)\), \(m=\frac{-1-0}{5 - 0}=-\frac{1}{5}\), which confirms the slope.

Answer:

\(-\frac{1}{5}\)