Algebra 1 - Slope and Rate of Change

Front

What is the slope formula?

Back

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

Front

What does an undefined slope indicate?

Back

An undefined slope indicates a vertical line, where the change in x is zero, making the slope formula result in division by zero.

Front

What is the slope of a horizontal line?

Back

The slope of a horizontal line is 0, indicating no change in y as x changes.

Front

How do you interpret a positive slope?

Back

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

Front

How do you interpret a negative slope?

Back

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

Front

What is the rate of change in a linear function?

Back

The rate of change in a linear function is the same as the slope, representing how much y changes for a unit change in x.

Front

Calculate the slope between the points (2, 3) and (4, 7).

Back

Using the slope formula: \( m = \frac{7 - 3}{4 - 2} = \frac{4}{2} = 2 \).

Front

What is the slope of the line represented by the equation \( y = 3x + 1 \)?

Back

The slope of the line is 3, which is the coefficient of x in the equation.

Front

If a line has a slope of \( \frac{1}{2} \), what does this mean in terms of rise over run?

Back

It means for every 2 units you move horizontally (run), the line rises 1 unit (rise).

Front

What is the slope of the line represented by the equation \( y = -2x + 4 \)?

Back

The slope of the line is -2, indicating a decrease in y as x increases.