Slope and Slope-Intercept Form

Front

What is the slope of a line?

Back

The slope of a line is a measure of its steepness, typically represented as 'm' in the slope-intercept form of a linear equation (y = mx + b). It is calculated as the change in y divided by the change in x (rise/run).

Front

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

Back

The slope-intercept form of a linear equation is given by the formula y = mx + b, where 'm' is the slope and 'b' is the y-intercept.

Front

How do you find the y-intercept from the equation y = -2x + 5?

Back

The y-intercept is the value of y when x = 0. In the equation y = -2x + 5, the y-intercept is 5.

Front

What is the formula to calculate the slope between two points (x1, y1) and (x2, y2)?

Back

The formula to calculate the slope (m) between two points is m = (y2 - y1) / (x2 - x1).

Front

If a line has a slope of 2, what does this indicate about the line's steepness?

Back

A slope of 2 indicates that for every 1 unit increase in x, the value of y increases by 2 units, making the line steep.

Front

What does a negative slope indicate about a line?

Back

A negative slope indicates that as x increases, y decreases, resulting in a line that slopes downward from left to right.

Front

What is the slope of the line that passes through the points (2, 4) and (6, 12)?

Back

The slope is 2, calculated using the formula m = (12 - 4) / (6 - 2).

Front

How do you determine the slope from a graph?

Back

To determine the slope from a graph, select two points on the line, find the rise (change in y) and run (change in x), and use the formula m = rise/run.

Front

What is the y-intercept of the line represented by the equation y = 3x - 7?

Back

The y-intercept is -7, which is the value of y when x = 0.

Front

What does it mean if a line has a slope of 0?

Back

A slope of 0 means the line is horizontal, indicating that there is no change in y as x changes.