Standard: 8.EE.5 - Slope
Description: Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. For example, compare a distance-time graph to a distance-time equation to determine which of two moving objects has greater speed. Vocabulary: Unit Rate - a comparison of two measurements in which one of the terms has a value of 1. Slope - How steep a straight line is. Also called "gradient". rise/run (change in y divided by the change in x). Proportional - When two quantities always have the same size in relation to each other. They have the same ratio. |
Standard: 8.EE.6 - Slope-intercept form of a line
Description: Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b. Vocabulary: Slope intercept form of a line - An equation that defines a straight line. y = mx+b; m=slope (R.O.C) b=y-intercept (initial value) Slope - Rise/Run (Change in y/change in x) y2-y1/x2-x1 y-intercept - Where the graph crosses the y axis. |
Standard: 8.F.1 -
Description: Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output. Vocabulary: Input - The x value in an equation. The independent variable. Output - The y value (f(x)) in an equation. The dependent variable. Function - A function relates an input to an output. It is a function if every input relates to exactly one output. Vertical Line Test - On a graph, the idea of single valued means that no vertical line ever crosses more than one value. if it crosses more than once it is still a valid curve, but is not a function. |
Standard: 8.F.2 -
Description: Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a linear function represented by a table of values and a linear function represented by an algebraic expression, determine which function has the greater rate of change. Vocabulary: Linear function - A function that makes a straight line when it is graphed. y=mx+b Rate of Change - Another name of slope. How one quantity changes in relation to another quantity. |
Standard: 8.F.3 -
Description: Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. For example, the function A = s2 giving the area of a square as a function of its side length is not linear because its graph contains the points (1,1), (2,4) and (3,9), which are not on a straight line. Vocabulary: Linear - An equation or graph that is a straight line. Nonlinear - An equation or graph that is not a straight line. Example: y = 1/x, y=x^2, y= 4^x |
Standard: 8.F.4 -
Description: Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values. Vocabulary: Rate of Change - Another name of slope. How one quantity changes in relation to another quantity. Initial Value - The starting value on a graph. Where the graph crosses the y-axis. |
Standard: 8.F.5 - Graphs from stories
Description: Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally. |