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Describing and Graphing Linear Functions, Equations, and Inequalities

6 dot points across 6 inquiry questions. Click any dot point for a focused answer with worked past exam questions where available.

How do you graph a linear function and identify its key features: the x-intercept, y-intercept, zeros, and slope?

Graph linear functions on the coordinate plane and identify key features, including x-intercept, y-intercept, zeros, and slope, in mathematical and real-world problems (TEKS A.3A).
A STAAR Algebra I answer on graphing linear functions and reading their key features (TEKS A.3A) - the x-intercept, y-intercept, zeros, and slope - from slope-intercept and standard form, including the hot-spot graphing item type.
10 min answer →

How do you graph the solution set of a linear inequality in two variables, choosing the boundary line style and the side to shade?

Graph the solution set of linear inequalities in two variables on the coordinate plane, using a solid or dashed boundary and shading the correct half-plane (TEKS A.3D).
A STAAR Algebra I answer on graphing linear inequalities in two variables (TEKS A.3D) - dashed versus solid boundary lines, choosing the half-plane to shade with a test point, and the hot-spot item type.
9 min answer →

How do you write the equation of a line parallel or perpendicular to a given line, and how do you set up and solve direct variation?

Write the equation of a line through a given point parallel or perpendicular to a given line, and write and solve equations involving direct variation (TEKS A.2D, A.2E, A.2F).
A STAAR Algebra I answer on parallel and perpendicular lines (equal slopes, negative-reciprocal slopes) and direct variation y equals kx (TEKS A.2D, A.2E, A.2F), with the constant of proportionality.
9 min answer →

How do you analyze a scatterplot, write a trend line, judge correlation, and use the model to make predictions?

Use scatterplots to analyze the relationship between two quantitative variables, write a trend-line equation by informal methods, judge its reasonableness, and make predictions, interpreting the correlation (TEKS A.3F, A.3G, A.4A, A.4B, A.4C).
A STAAR Algebra I answer on scatterplots, writing a trend line, correlation (positive, negative, none, and the correlation coefficient r), and making predictions (TEKS A.3F, A.3G, A.4A, A.4B, A.4C).
10 min answer →

How do you find the slope and rate of change of a linear function from a table, a graph, two points, or a context, and interpret it?

Calculate the rate of change (slope) of a linear function represented tabularly, graphically, or algebraically, and interpret slope and intercepts as rate and initial value in context (TEKS A.3A, A.3B).
A STAAR Algebra I answer on finding slope and rate of change from tables, graphs, two points, and contexts (TEKS A.3A, A.3B), the slope formula on the reference sheet, and interpreting slope and intercepts in real-world situations.
10 min answer →

How do you write a linear equation in slope-intercept, point-slope, and standard form from points, a graph, a table, or a description?

Write linear equations in two variables in various forms ( $y = mx + b$ , $Ax + By = C$ , $y - y_1 = m(x - x_1)$ ) given one point and the slope, two points, a table, a graph, or a verbal description (TEKS A.2B, A.2C, A.2G).
A STAAR Algebra I answer on writing linear equations in slope-intercept, point-slope, and standard form (TEKS A.2B, A.2C, A.2G) from a point and slope, two points, a table, a graph, or a verbal description.
10 min answer →