Question

1. choose efficient methods how can you find the slope of the line that passes through the points (0, 0) and (2, 4)? explain.

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 the points

Here, \( (x_1, y_1)=(0, 0) \) and \( (x_2, y_2)=(2, 4) \).

Step3: Substitute into formula

Substitute the values into the slope formula: \( m=\frac{4 - 0}{2 - 0}=\frac{4}{2}=2 \).
Another way: Since one point is the origin \((0,0)\), we can use the concept of slope as rise over run, where rise is the change in \( y \) and run is the change in \( x \). From \((0,0)\) to \((2,4)\), the rise is \( 4 - 0 = 4 \) and the run is \( 2 - 0 = 2 \), so slope \(=\frac{4}{2}=2\).

Answer:

The slope of the line passing through \((0, 0)\) and \((2, 4)\) is \( 2 \). We can find it using the slope formula \( m=\frac{y_2 - y_1}{x_2 - x_1} \) (substituting \( (x_1,y_1)=(0,0) \) and \( (x_2,y_2)=(2,4) \) gives \( m = \frac{4 - 0}{2 - 0}=2 \)) or by using rise over run (rise is \( 4 \), run is \( 2 \), so \( \frac{4}{2}=2 \)).