Question

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

Explanation:

Step1: Identify two points on the line

We can see that the line passes through the origin \((0, 0)\) and another point, for example, \((1, 1)\) (or we can use other points like \((2, 2)\), \((3, 3)\) etc.). Let's take \((x_1, y_1) = (0, 0)\) and \((x_2, y_2) = (1, 1)\).

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 the formula \(m=\frac{y_2 - y_1}{x_2 - x_1}\).

Substituting the values \(x_1 = 0\), \(y_1 = 0\), \(x_2 = 1\), \(y_2 = 1\) into the formula:

\(m=\frac{1 - 0}{1 - 0}=\frac{1}{1} = 1\)

We can also check with another pair of points, say \((0,0)\) and \((2,2)\). Then \(m=\frac{2 - 0}{2 - 0}=\frac{2}{2}=1\), which confirms the slope.

Answer:

\(1\)