Linear Functions and Desmos

Front

What is a linear function?

Back

A linear function is a function that can be graphically represented as a straight line. It has the form f(x) = mx + b, where m is the slope and b is the y-intercept.

Front

What does the slope of a linear function represent?

Back

The slope (m) of a linear function represents the rate of change of the function. It indicates how much the y-value changes for a unit change in the x-value.

Front

What is the y-intercept of a linear function?

Back

The y-intercept (b) of a linear function is the point where the graph intersects the y-axis. It represents the value of f(x) when x = 0.

Front

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

Back

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

Front

What is the standard form of a linear equation?

Back

The standard form of a linear equation is Ax + By = C, where A, B, and C are integers, and A should be non-negative.

Front

How can you determine if two lines are parallel?

Back

Two lines are parallel if they have the same slope (m) but different y-intercepts (b).

Front

What does it mean for two lines to be perpendicular?

Back

Two lines are perpendicular if the product of their slopes is -1. This means that if one line has a slope of m, the other line's slope will be -1/m.

Front

What is the purpose of using Desmos in graphing linear functions?

Back

Desmos is an online graphing calculator that allows users to visualize linear functions, explore their properties, and interactively manipulate equations to see real-time changes in graphs.

Front

How can you graph a linear function using its slope and y-intercept?

Back

To graph a linear function, start at the y-intercept (0, b) on the y-axis. From there, use the slope (rise/run) to find another point on the line and draw a straight line through these points.

Front

What is a function in mathematical terms?

Back

A function is a relation that assigns exactly one output (y) for each input (x). It can be represented as a set of ordered pairs, a graph, or an equation.