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., since the line has a constant slope). 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 \(x_1 = 0\), \(y_1 = 0\), \(x_2 = 1\), and \(y_2 = 1\) into the formula, we get:

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

We can also check with other points. For example, take \((x_1,y_1)=(0,0)\) and \((x_2,y_2)=(2,2)\). Then \(m=\frac{2 - 0}{2 - 0}=\frac{2}{2}=1\), which confirms the slope.

Answer:

\(1\)