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, leading to division by zero in the slope formula.

Front

What does a slope of zero indicate?

Back

A slope of zero indicates a horizontal line, where there is no change in y as x changes.

Front

How do you find the slope between two points?

Back

To find the slope between two points, use the slope formula: \( m = \frac{y_2 - y_1}{x_2 - x_1} \).

Front

What is the slope of the line represented by the equation \( y = -\frac{3}{2}x + 4 \)?

Back

The slope of the line is \( m = -\frac{3}{2} \).

Front

Calculate the slope between the points (2, 4) and (-1, 4).

Back

The slope is \( m = \frac{4 - 4}{-1 - 2} = 0 \).

Front

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

Back

The slope is undefined because the x-coordinates are the same, indicating a vertical line.

Front

What is the slope of a line that rises 4 units for every 5 units it runs?

Back

The slope is \( m = \frac{4}{5} \).

Front

What is the slope of a line that falls 5 units for every 7 units it runs?

Back

The slope is \( m = -\frac{5}{7} \).

Front

If a line has a slope of \( m = \frac{2}{3} \), what does this mean?

Back

This means that for every 3 units the line moves horizontally to the right, it moves 2 units up.