Unit 1 Review--Function Basics and 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 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

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

Back

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

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

What does it mean for two lines to be parallel?

Back

Two lines are parallel if they have the same slope and will never intersect.

Front

How do you write the equation of a line parallel to a given line?

Back

To write the equation of a line parallel to a given line, use the same slope as the given line and substitute the coordinates of the point through which the new line passes into the slope-intercept form.

Front

What is a y-intercept?

Back

The y-intercept is the point where a line crosses the y-axis, represented as (0, b) in the slope-intercept form y = mx + b.

Front

What is a linear equation?

Back

A linear equation is an equation that represents a straight line when graphed. It can be written in various forms, including slope-intercept form and standard form.

Front

What is a step function?

Back

A step function is a piecewise constant function that jumps from one value to another, creating a staircase-like graph.

Front

How do you convert a linear equation from standard form to slope-intercept form?

Back

To convert from standard form (Ax + By = C) to slope-intercept form (y = mx + b), solve for y in terms of x.

Front

What is the significance of the slope in real-world applications?

Back

The slope can represent rates of change, such as speed, cost per item, or growth rates in various real-world scenarios.