# Graphing Equations

Determining intercepts from graph, table, and equations and interpreting real-world meanings. Calculating slope from two points or a table and classifying slope as positive, negative, zero, or undefined. Classifying lines as perpendicular or parallel using slope. Determining rate of change from a graph and finding average rate of change from real-world situations. Writing equations in slope-intercept, point-slope and standard form and making comparisons of linear functions given table, graph, or equation focusing on slope and intercepts.

Graph linear and quadratic functions and show intercepts, maxima, and minima. Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line). For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table). Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph. Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point). Write a function that describes a relationship between two quantities. Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function.