Slope: Tables & Slope Formula

Front

What is the definition of slope?

Back

Slope is a measure of the steepness or incline of a line, typically represented as the ratio of the vertical change (rise) to the horizontal change (run) between two points on the line.

Front

What is the slope formula?

Back

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

Front

How do you find the slope from a table of values?

Back

To find the slope from a table, select two points (x1, y1) and (x2, y2) from the table and use the slope formula: \( m = \frac{y_2 - y_1}{x_2 - x_1} \).

Front

What does a positive slope indicate?

Back

A positive slope indicates that as the x-value increases, the y-value also increases, showing a direct relationship.

Front

What does a negative slope indicate?

Back

A negative slope indicates that as the x-value increases, the y-value decreases, showing an inverse relationship.

Front

What does an undefined slope mean?

Back

An undefined slope occurs when a line is vertical, meaning there is no horizontal change (run = 0), making the slope calculation impossible.

Front

What is the slope of a horizontal line?

Back

The slope of a horizontal line is 0, indicating that there is no vertical change as the x-value changes.

Front

Calculate the slope between the points (2, 3) and (5, 11).

Back

Using the slope formula: \( m = \frac{11 - 3}{5 - 2} = \frac{8}{3} \).

Front

What is the slope of the line represented by the equation y = 2x + 1?

Back

The slope of the line is 2, which is the coefficient of x in the equation.

Front

If the slope of a line is \( \frac{-3}{4} \), what does this indicate about the line?

Back

This indicates that for every 4 units the line moves to the right (positive x-direction), it moves down 3 units (negative y-direction).