Question

1. reasoning how can you find the slope of the line that passes through the points (0, 0) and (2, 4)? explain.
2. the points (2.1, -4.2) and (2.5, -5) form a proportional relationship. what is the slope of the line that passes through these two points?
3. find the slope of the line.

(there is a coordinate grid with a line plotted on it, labeled with x and y axes from -8 to 8, and the line passes through the origin and other points like (2, 2) and (4, 4) approximately (visually from the grid))
2-6 connect proportional relationships and slope

Explanation:

Question 8

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: \( m=\frac{4 - 0}{2 - 0}=\frac{4}{2} = 2 \).
To explain, we use the slope formula which calculates the rate of change of \( y \) with respect to \( x \). By taking the difference in \( y \)-coordinates and dividing by the difference in \( x \)-coordinates of the two points, we find the slope.

Step1: Recall slope formula

The slope \( m \) of a line passing through two points \((x_1, y_1)\) and \((x_2, y_2)\) is \( m=\frac{y_2 - y_1}{x_2 - x_1} \).

Step2: Identify the points

Given points \((x_1, y_1)=(2.1, - 4.2)\) and \((x_2, y_2)=(2.5, - 5)\).

Step3: Substitute into formula

Substitute the values: \( m=\frac{-5-(-4.2)}{2.5 - 2.1}=\frac{-5 + 4.2}{0.4}=\frac{-0.8}{0.4}=- 2 \).

Step1: Identify two points on the line

From the graph, we can see that the line passes through \((0,0)\) and \((2,2)\) (or other pairs like \((4,4)\), etc.). Let's take \((x_1, y_1)=(0, 0)\) and \((x_2, y_2)=(2, 2)\).

Step2: Recall slope formula

The slope \( m=\frac{y_2 - y_1}{x_2 - x_1} \).

Step3: Substitute into formula

Substitute the values: \( m=\frac{2 - 0}{2 - 0}=\frac{2}{2}=1 \).

Answer:

The slope is calculated using the formula \( m=\frac{y_2 - y_1}{x_2 - x_1} \). Substituting \((x_1,y_1)=(0,0)\) and \((x_2,y_2)=(2,4)\), we get \( m = \frac{4 - 0}{2 - 0}=2 \). So the slope of the line is \( 2 \).

Question 9