Slope & Linear Functions

Front

What is the definition of slope in a linear function?

Back

The slope of a linear function is a measure of the steepness of the line, calculated as the change in the y-coordinate divided by the change in the x-coordinate (rise over run).

Front

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

Back

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

Front

What does a positive slope indicate about a linear function?

Back

A positive slope indicates that as the x-values increase, the y-values also increase, resulting in an upward slant of the line.

Front

What does a negative slope indicate about a linear function?

Back

A negative slope indicates that as the x-values increase, the y-values decrease, resulting in a downward slant of the line.

Front

What does an undefined slope mean in the context of a linear function?

Back

An undefined slope occurs when a line is vertical, meaning the x-values are the same for all points on the line, leading to division by zero in the slope formula.

Front

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

Back

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

Front

How can you determine if a relationship is linear from a set of data points?

Back

A relationship is linear if the data points can be plotted on a graph and form a straight line.

Front

What is the significance of the y-intercept in a linear function?

Back

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

Front

How do you find the slope of a line given its equation in standard form (Ax + By = C)?

Back

To find the slope from the standard form, rearrange the equation into slope-intercept form (y = mx + b) and identify the coefficient of x as the slope.

Front

What is the relationship between parallel lines in terms of slope?

Back

Parallel lines have the same slope, meaning they never intersect and maintain a constant distance apart.