Question

line m goes through points a and b. what is the slope of line m? now, use the coordinates to write an expression you could use to find the change in vertical distance for a given change in horizontal distance. point a: (3, 2) point b: (8, 5) slope = \\(\frac{\text{vertical distance}}{\text{horizontal distance}} = \frac{\text{change in } y\text{-values}}{\text{change in } x\text{-values}}\\) = \\(\frac{\square - \square}{\square - \square}\\)

Explanation:

Step1: Recall slope formula

The slope formula is \( \text{slope} = \frac{y_2 - y_1}{x_2 - x_1} \), where \((x_1, y_1)\) and \((x_2, y_2)\) are two points on the line.

Step2: Identify coordinates

For point A \((3, 2)\) and point B \((8, 5)\), we have \(x_1 = 3\), \(y_1 = 2\), \(x_2 = 8\), \(y_2 = 5\).

Step3: Substitute into formula

Substitute the values into the slope formula. The change in y - values (vertical distance) is \(y_2 - y_1=5 - 2\), and the change in x - values (horizontal distance) is \(x_2 - x_1 = 8 - 3\). So the expression for slope is \(\frac{5 - 2}{8 - 3}\).

Answer:

\(\frac{5 - 2}{8 - 3}\) (and the slope calculation would be \(\frac{3}{5}=0.6\), but the expression as per the question is \(\frac{5 - 2}{8 - 3}\))