13 8.FGR.5.1 Math.8.F.1 8.FGR.5.1 8.FGR.5.1 8.FGR.5.1 8.F.1 8.FGR.1 8.FGR.1 8.FGR.5.1 8.FGR.5.1 15 Math.8.F.2 8.FGR.5.4 8.FGR.5.4 8.F.2 8.FGR.4 8.FGR.5.4 14 8.FGR.5.5 Math.8.F.3 8.FGR.5.5 8.FGR.5.5 8.F.3 8.FGR.5 8.FGR.5.5 17 Math.8.F.5 8.FGR.5.9 8.FGR.5.9 8.F.5 8.FGR.9 CC.2.2.8.C.1 M08.B-F.1.1.1 M08.B-F.1.1.2 M08.B-F.1.1.3 M08.B-F.2.1.2 MA.8.F.1.1 MA.8.F.1.2 MA.8.F.1.3 8.FGR.5.1 8.FGR.5.2 8.FGR.5.3 8.FGR.5.4 8.FN.3 8.FN.4 8.FN.5 8.FN.6 8.FN.7 8.FN.8 8.FN.9

Functions 8th Grade

Georgia Standards: 8.FGR.5.1
Show and explain that a function is a rule that assigns to each input exactly one output.
Georgia Standards: 8.FGR.5.4
Compare properties (rate of change and initial value) of two functions used to model an authentic situation each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).
Georgia Standards: 8.FGR.5.5
Write and explain the equations y = mx + b (slope-intercept form), Ax + By = C (standard form), and (y - y₁) = m(x-x₁) (point-slope form) as defining a linear function whose graph is a straight line to reveal and explain different properties of the function.
Georgia Standards: 8.FGR.5.9
Graph and analyze linear functions expressed in various algebraic forms and show key characteristics of the graph to describe applicable situations.
Georgia Standards: 8.FGR.5.1
Show and explain that a function is a rule that assigns to each input exactly one output.
Georgia Standards: 8.FGR.5.2
Within realistic situations, identify and describe examples of functions that are linear or nonlinear. Sketch a graph that exhibits the qualitative features of a function that has been described verbally.
Georgia Standards: 8.FGR.5.3
Relate the domain of a linear function to its graph and where applicable to the quantitative relationship it describes.
Georgia Standards: 8.FGR.5.4
Compare properties (rate of change and initial value) of two functions used to model an authentic situation each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).

A linear function is a function which can be written in the form y = mx + b, where m is the slope and b is where the line crosses the y-axis.

The point where a line crosses the y-axis is called the y-intercept.
At this point, the x-value is 0.

The table, graph, and equation each represent the same line.
The y-intercept of the line is (0, 1).

x	y
-2	-1
-1	0
0	1
1	2

y = x + 1

The slope of a line is also called the rate of change. Given two points on a line, (x_₁, y_₁) and (x_₂, y_₂), the slope is the ratio of the change in y to the change in x.

m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}

In the equation above, y = x + 1, the slope is the coefficient on x, which is 1.

In the table above, choose any two points to find the slope.
The calculation below shows finding the slope using the points (0, 1) and (1, 2).

\begin{array}{rcl} m & = & \frac{2 - 1}{1 - 0} \\ = & \frac{1}{1} \\ = & 1 \end{array}

In the graph above, choose any two points to find the slope.
The calculation below shows finding the slope using the points (1, 2) and (2, 3).

\begin{array}{rcl} m & = & \frac{3 - 2}{2 - 1} \\ = & \frac{1}{1} \\ = & 1 \end{array}

A linear function is a function which can be written in the form y = mx + b.
If a function cannot be written in this form, it is referred to as nonlinear.

The graphs of linear functions are straight lines.
The graphs of nonlinear functions are not straight lines.

y = 3 x + 8

y = 3 x^{2} + 8

y = \frac{1}{3} x

C = 2 π r

linear

nonlinear

linear


linear		nonlinear

Functions

Georgia Standards: 8.FGR.5.1

Show and explain that a function is a rule that assigns to each input exactly one output.

Georgia Standards: 8.FGR.5.4

Compare properties (rate of change and initial value) of two functions used to model an authentic situation each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).

Georgia Standards: 8.FGR.5.5

Write and explain the equations y = mx + b (slope-intercept form), Ax + By = C (standard form), and (y - y₁) = m(x-x₁) (point-slope form) as defining a linear function whose graph is a straight line to reveal and explain different properties of the function.

Georgia Standards: 8.FGR.5.9

Graph and analyze linear functions expressed in various algebraic forms and show key characteristics of the graph to describe applicable situations.

Georgia Standards: 8.FGR.5.1

Show and explain that a function is a rule that assigns to each input exactly one output.

Georgia Standards: 8.FGR.5.2

Within realistic situations, identify and describe examples of functions that are linear or nonlinear. Sketch a graph that exhibits the qualitative features of a function that has been described verbally.

Georgia Standards: 8.FGR.5.3

Relate the domain of a linear function to its graph and where applicable to the quantitative relationship it describes.

Georgia Standards: 8.FGR.5.4

Compare properties (rate of change and initial value) of two functions used to model an authentic situation each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).

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Functions

Georgia Standards: 8.FGR.5.1

Show and explain that a function is a rule that assigns to each input exactly one output.

Georgia Standards: 8.FGR.5.4

Compare properties (rate of change and initial value) of two functions used to model an authentic situation each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).

Georgia Standards: 8.FGR.5.5

Write and explain the equations y = mx + b (slope-intercept form), Ax + By = C (standard form), and (y - y1) = m(x-x1) (point-slope form) as defining a linear function whose graph is a straight line to reveal and explain different properties of the function.

Georgia Standards: 8.FGR.5.9

Graph and analyze linear functions expressed in various algebraic forms and show key characteristics of the graph to describe applicable situations.

Georgia Standards: 8.FGR.5.1

Show and explain that a function is a rule that assigns to each input exactly one output.

Georgia Standards: 8.FGR.5.2

Within realistic situations, identify and describe examples of functions that are linear or nonlinear. Sketch a graph that exhibits the qualitative features of a function that has been described verbally.

Georgia Standards: 8.FGR.5.3

Relate the domain of a linear function to its graph and where applicable to the quantitative relationship it describes.

Georgia Standards: 8.FGR.5.4

Compare properties (rate of change and initial value) of two functions used to model an authentic situation each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).

Processing Request...

Write and explain the equations y = mx + b (slope-intercept form), Ax + By = C (standard form), and (y - y₁) = m(x-x₁) (point-slope form) as defining a linear function whose graph is a straight line to reveal and explain different properties of the function.