Identifying Slope and Intercepts Linear Functions

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 equation of a line (y = mx + b). It is calculated as the change in y divided by the change in x (rise/run).

Front

How do you find the y-intercept of a linear equation?

Back

To find the y-intercept of a linear equation in the form y = mx + b, set x to 0 and solve for y. The y-intercept is the point where the line crosses the y-axis.

Front

What is the x-intercept of a linear function?

Back

The x-intercept is the point where the line crosses the x-axis. To find it, set y to 0 in the equation and solve for x.

Front

What does the equation y = mx + b represent?

Back

This is the slope-intercept form of a linear equation, where 'm' is the slope and 'b' is the y-intercept.

Front

True or False: The slope can be negative, positive, or zero.

Back

True. A negative slope indicates a downward trend, a positive slope indicates an upward trend, and a slope of zero indicates a horizontal line.

Front

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

Back

The slope (m) can be calculated using the formula m = (y2 - y1) / (x2 - x1).

Front

What is the significance of the y-intercept in a graph?

Back

The y-intercept indicates the value of y when x is zero, showing where the line crosses the y-axis.

Front

If a line has a slope of 0, what does that mean?

Back

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

Front

What is the relationship between the slope and the angle of a line?

Back

The slope of a line is related to the angle it makes with the x-axis; a steeper slope corresponds to a larger angle.

Front

How can you find both intercepts from the equation 4x - 10y = 20?

Back

To find the x-intercept, set y to 0 and solve for x. To find the y-intercept, set x to 0 and solve for y.