Students use linear equations and systems of linear equations to represent, analyze, and solve a variety of problems. Students recognize equations for proportions (๐บ/๐น = ๐ฎ or ๐บ = ๐ฎ๐น) as special linear equations (๐บ = ๐ฎ๐น + ๐ฃ), understanding that the constant of proportionality (๐ฎ) is the slope, and the graphs are lines through the origin. They understand that the slope (๐ฎ) of a line is a constant rate of change, so that if the input or ๐น-coordinate changes by an amount ๐, the output or ๐บ-coordinate changes by the amount ๐ฎยท๐. Students also use a linear equation to describe the association between two quantities in bivariate data (such as arm span vs. height for students in a classroom). At this grade, fitting the model, and assessing its fit to the data are done informally. Interpreting the model in the context of the data requires students to express a relationship between the two quantities in question and to interpret components of the relationship (such as slope and ๐บ-intercept) in terms of the situation. Students strategically choose and efficiently implement procedures to solve linear equations in one variable, understanding that when they use the properties of equality and the concept of logical equivalence, they maintain the solutions of the original equation. Students solve systems of two linear equations in two variables and relate the systems to pairs of lines in the plane; these intersect, are parallel, or are the same line. Students use linear equations, systems of linear equations, linear functions, and their understanding of slope of a line to analyze situations and solve problems.

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Students use linear equations and systems of linear equations to represent, analyze, and solve a variety of problems. Students recognize equations for proportions (๐บ/๐น = ๐ฎ or ๐บ = ๐ฎ๐น) as special linear equations (๐บ = ๐ฎ๐น + ๐ฃ), understanding that the constant of proportionality (๐ฎ) is the slope, and the graphs are lines through the origin. They understand that the slope (๐ฎ) of a line is a constant rate of change, so that if the input or ๐น-coordinate changes by an amount ๐, the output or ๐บ-coordinate changes by the amount ๐ฎยท๐. Students also use a linear equation to describe the association between two quantities in bivariate data (such as arm span vs. height for students in a classroom). At this grade, fitting the model, and assessing its fit to the data are done informally. Interpreting the model in the context of the data requires students to express a relationship between the two quantities in question and to interpret components of the relationship (such as slope and ๐บ-intercept) in terms of the situation. Students strategically choose and efficiently implement procedures to solve linear equations in one variable, understanding that when they use the properties of equality and the concept of logical equivalence, they maintain the solutions of the original equation. Students solve systems of two linear equations in two variables and relate the systems to pairs of lines in the plane; these intersect, are parallel, or are the same line. Students use linear equations, systems of linear equations, linear functions, and their understanding of slope of a line to analyze situations and solve problems.

Students use linear equations and systems of linear equations to represent, analyze, and solve a variety of problems. Students recognize equations for proportions (๐บ/๐น = ๐ฎ or ๐บ = ๐ฎ๐น) as special linear equations (๐บ = ๐ฎ๐น + ๐ฃ), understanding that the constant of proportionality (๐ฎ) is the slope, and the graphs are lines through the origin. They understand that the slope (๐ฎ) of a line is a constant rate of change, so that if the input or ๐น-coordinate changes by an amount ๐, the output or ๐บ-coordinate changes by the amount ๐ฎยท๐. Students also use a linear equation to describe the association between two quantities in bivariate data (such as arm span vs. height for students in a classroom). At this grade, fitting the model, and assessing its fit to the data are done informally. Interpreting the model in the context of the data requires students to express a relationship between the two quantities in question and to interpret components of the relationship (such as slope and ๐บ-intercept) in terms of the situation. Students strategically choose and efficiently implement procedures to solve linear equations in one variable, understanding that when they use the properties of equality and the concept of logical equivalence, they maintain the solutions of the original equation. Students solve systems of two linear equations in two variables and relate the systems to pairs of lines in the plane; these intersect, are parallel, or are the same line. Students use linear equations, systems of linear equations, linear functions, and their understanding of slope of a line to analyze situations and solve problems.

Students use linear equations and systems of linear equations to represent, analyze, and solve a variety of problems. Students recognize equations for proportions (๐บ/๐น = ๐ฎ or ๐บ = ๐ฎ๐น) as special linear equations (๐บ = ๐ฎ๐น + ๐ฃ), understanding that the constant of proportionality (๐ฎ) is the slope, and the graphs are lines through the origin. They understand that the slope (๐ฎ) of a line is a constant rate of change, so that if the input or ๐น-coordinate changes by an amount ๐, the output or ๐บ-coordinate changes by the amount ๐ฎ ร ๐. Students also use a linear equation to describe the association between two quantities in bivariate data (such as arm span vs. height for students in a classroom). At this grade, fitting the model and assessing its fit to the data are done informally. Interpreting the model in the context of the data requires students to express a relationship between the two quantities in question and to interpret components of the relationship (such as slope and ๐บ-intercept) in terms of the situation. Students strategically choose and efficiently implement procedures to solve linear equations in one variable, understanding that when they use the properties of equality and the concept of logical equivalence, they maintain the solutions of the original equation. Students solve systems of two linear equations in two variables and relate the systems to pairs of lines in the plane; these intersect, are parallel, or are the same line. Students use linear equations, systems of linear equations, linear functions, and their understanding of slope of a line to analyze situations and solve problems.