# Algebra 1 – Unit 4 – Linear Equations and Inequalities

## Standards

 Standard Language A.CED.2 Create equations in two or more variables to present relationships between quantities; graph equations on coordinate axes with labels and scales. A.REI.10 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). A.REI.12 Graph the solutions to a linear inequality in two variables as a half plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables ad the intersection of the corresponding half-planes. F.IF.6 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. S.ID.1 Represent data with plots on the real number line (dot plots, histograms, and box plots). S.ID.2 Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets. S.ID.3 Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers). S.ID.6c Fit a linear function for a scatter plot that suggests a linear association. S.ID.7 Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data.

## The “Story” of This Unit

Data can be messy, but there are patterns everywhere! When we look at a scatter plot, all we see is a bunch of dots…can we make any conclusions from these things. Sometimes, the answer is clearly YES…we can use data to create equations (sometimes just by drawing a graphical picture) and we can use that information to make claims about what is likely to happen in the future based on this trend. We will extend our understanding of functions by collecting a lot of inputs and noticing they have a common additive growth over time. Looking at patterns, we will find that complicated things can be made more simple by considering the average change that happens over time. Math is incredibly powerful at using patterns to predict the future.

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