Flashcard Slope and Intercepts

Front

What is the definition of slope in a linear equation?

Back

The slope is a measure of the steepness of a line, calculated as the change in y (vertical) divided by the change in x (horizontal).

Front

How do you calculate the slope between two points (x1, y1) and (x2, y2)?

Back

Slope (m) = (y2 - y1) / (x2 - x1).

Front

What is the formula for the slope-intercept form of a linear equation?

Back

The slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.

Front

What does the y-intercept represent in a linear equation?

Back

The y-intercept is the point where the line crosses the y-axis, represented by the value of y when x = 0.

Front

If a line has a slope of 0, what does that indicate about the line?

Back

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

Front

If a line has an undefined slope, what does that indicate about the line?

Back

An undefined slope indicates a vertical line, meaning x remains constant while y changes.

Front

Find the slope of the line that passes through the points (2, 3) and (4, 7).

Back

Slope = (7 - 3) / (4 - 2) = 4/2 = 2.

Front

Find the slope of the line that passes through the points (1, 2) and (3, 6).

Back

Slope = (6 - 2) / (3 - 1) = 4/2 = 2.

Front

What is the slope of a line that rises 3 units for every 4 units it runs?

Back

The slope is 3/4.

Front

What is the slope of a line that falls 2 units for every 1 unit it runs?

Back

The slope is -2.