Question

what is the slope of this line? simplify your answer and write it as a proper fraction, improper fraction, or integer.

Explanation:

Step1: Recall slope formula

The slope \( m \) of a line passing through two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by \( m=\frac{y_2 - y_1}{x_2 - x_1} \).

Step2: Identify two points on the line

From the graph, the line passes through the origin \((0, 0)\) and another point, say \((6, 3)\) (we can also choose other points like \((-8, -4)\), but \((6, 3)\) is easy to read). Let \((x_1, y_1)=(0, 0)\) and \((x_2, y_2)=(6, 3)\).

Step3: Calculate the slope

Substitute the values into the slope formula: \( m=\frac{3 - 0}{6 - 0}=\frac{3}{6} \). Simplify the fraction: \( \frac{3}{6}=\frac{1}{2} \). We can also check with another point, for example, \((-8, -4)\) and \((0, 0)\): \( m=\frac{0 - (-4)}{0 - (-8)}=\frac{4}{8}=\frac{1}{2} \), which confirms the slope.

Answer:

\(\frac{1}{2}\)