Question

question 2
part a
you can also find slope without looking at a graph. using only the points you selected, write two numerical expressions: one to calculate the rise and the other to calculate the run. do not perform any operations; just write the expressions.

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part b
write a numerical expression for the slope using the expressions you wrote in part a.

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Explanation:

Part A

To find the rise and run between two points \((x_1, y_1)\) and \((x_2, y_2)\), the rise is the difference in the \(y\)-values and the run is the difference in the \(x\)-values.

Step 1: Calculate the rise

The rise is the vertical change, so we subtract the \(y\)-coordinates of the two points. If the two points are \((x_1, y_1)\) and \((x_2, y_2)\), the expression for the rise is \(y_2 - y_1\).

Step 2: Calculate the run

The run is the horizontal change, so we subtract the \(x\)-coordinates of the two points. The expression for the run is \(x_2 - x_1\).

Part B

The slope of a line is defined as the ratio of the rise to the run. So we use the expressions for rise and run from Part A.

Step 1: Define slope formula

The slope \(m\) is given by the formula \(m=\frac{\text{rise}}{\text{run}}\).

Step 2: Substitute rise and run expressions

Substituting the expressions for rise (\(y_2 - y_1\)) and run (\(x_2 - x_1\)) from Part A, the numerical expression for the slope is \(\frac{y_2 - y_1}{x_2 - x_1}\).

Part A Answer:

Rise: \(y_2 - y_1\)
Run: \(x_2 - x_1\)

Part B Answer:

\(\frac{y_2 - y_1}{x_2 - x_1}\)

Answer:

The slope of a line is defined as the ratio of the rise to the run. So we use the expressions for rise and run from Part A.

Step 1: Define slope formula

The slope \(m\) is given by the formula \(m=\frac{\text{rise}}{\text{run}}\).

Step 2: Substitute rise and run expressions

Substituting the expressions for rise (\(y_2 - y_1\)) and run (\(x_2 - x_1\)) from Part A, the numerical expression for the slope is \(\frac{y_2 - y_1}{x_2 - x_1}\).

Part A Answer:

Rise: \(y_2 - y_1\)
Run: \(x_2 - x_1\)

Part B Answer:

\(\frac{y_2 - y_1}{x_2 - x_1}\)