Question

slope of a line given a graph find the slope of the line graphed to the left. a. ( m = -\frac{2}{5} ) b. ( m = \frac{2}{5} ) c. ( m = -\frac{5}{2} ) d. ( m = \frac{5}{2} )

Explanation:

Step1: Identify two points on the line

From the graph, we can see two clear points: \((0, -2)\) and \((5, 0)\) (or we can also use \((-5, -4)\) and \((0, -2)\), but let's use \((0, -2)\) and \((5, 0)\) for simplicity).

Step2: Use the slope formula

The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Let \((x_1,y_1)=(0, -2)\) and \((x_2,y_2)=(5, 0)\). Then:
\(m=\frac{0 - (-2)}{5 - 0}=\frac{0 + 2}{5}=\frac{2}{5}\)
We can also check with another pair of points, say \((-5, -4)\) and \((0, -2)\). Let \((x_1,y_1)=(-5, -4)\) and \((x_2,y_2)=(0, -2)\). Then:
\(m=\frac{-2 - (-4)}{0 - (-5)}=\frac{-2 + 4}{5}=\frac{2}{5}\)

Answer:

B. \(m = \frac{2}{5}\)