Question

mental math using the slope formula, find the slope of the line through the points (0,0) and (3,6) use pencil and paper. explain how you can use mental math to find the slope of the line. the slope of the line is \boxed{} (type an integer or a simplified fraction.)

Explanation:

Step1: Recall slope formula

The slope \( m \) between 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 the points

Here, \( (x_1, y_1)=(0, 0) \) and \( (x_2, y_2)=(3, 6) \).

Step3: Substitute into formula

Substitute the values into the slope formula: \( m=\frac{6 - 0}{3 - 0}=\frac{6}{3} \).

Step4: Simplify the fraction

Simplify \( \frac{6}{3} \) to get \( 2 \).

For mental math: Notice that from \( (0,0) \) to \( (3,6) \), the rise (change in \( y \)) is \( 6 \) and the run (change in \( x \)) is \( 3 \). So slope is rise over run, \( \frac{6}{3}=2 \).

Answer:

\( 2 \)