Linear Functions and Desmos

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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.

Tags

CCSS.8.F.B.4

CCSS.HSF.LE.A.2

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What does the slope of a linear function represent?

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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.

Tags

CCSS.8.EE.B.5

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What is the y-intercept of a linear function?

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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.

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

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

Tags

CCSS.8.EE.B.5

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What is the standard form of a linear equation?

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

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How can you determine if two lines are parallel?

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

Tags

CCSS.8.EE.B.6

Front

What does it mean for two lines to be perpendicular?

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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.

Tags

CCSS.8.EE.B.6

Front

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

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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.

Tags

CCSS.HSF-IF.C.7A

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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.

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What is a function in mathematical terms?

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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.

Tags

CCSS.8.F.A.1