Question

a line passes through the origin and the point (3,5). what is the slope of the line? (-\frac{3}{5}) 0 (\frac{3}{5}) (\frac{5}{3})

Explanation:

Step1: Recall slope formula

The slope \( m \) between two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is \( m=\frac{y_2 - y_1}{x_2 - x_1} \).

Step2: Identify points

The origin is \( (0, 0) \) and the other point is \( (3, 5) \). So \( x_1 = 0,y_1 = 0,x_2 = 3,y_2 = 5 \).

Step3: Calculate slope

Substitute into the formula: \( m=\frac{5 - 0}{3 - 0}=\frac{5}{3} \).

Answer:

\(\frac{5}{3}\) (corresponding to the last option)