Slope and Proportional Relationships

Front

What does the slope represent in a real-world context?

Back

The slope represents the rate of change between two variables, indicating how much one variable changes in relation to another.

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

Find the slope of the line connecting the points (2, 3) and (4, 7).

Back

The slope is \( m = \frac{7 - 3}{4 - 2} = \frac{4}{2} = 2 \).

Front

What does a positive slope indicate about a line?

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 about a line?

Back

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

Front

How do you interpret a slope of 0?

Back

A slope of 0 indicates a horizontal line, meaning there is no change in the y-value as the x-value changes.

Front

How do you interpret an undefined slope?

Back

An undefined slope indicates a vertical line, meaning the x-value does not change while the y-value can vary.

Front

Find the slope of the line represented by the equation y = 3x + 2.

Back

The slope is 3, which means for every 1 unit increase in x, y increases by 3 units.

Front

What is the slope of a line that runs parallel to the line y = -2x + 5?

Back

The slope of a parallel line is also -2.

Front

What is the slope of a line that runs perpendicular to the line y = 4x - 1?

Back

The slope of a perpendicular line is \( -\frac{1}{4} \).