Linear Functions – Multiple Representations Worksheet

Convert a linear equation between standard form, slope-intercept form, and point-slope form.

Determine the x-intercept, y-intercept, and slope of a line from any one of its given representations.

Generate a table of values and a graph for a line from an equation, and vice versa.

Construct an original linear function and represent it across all of these forms.

Assign one or two functions per class period rather than all nine at once, since each chart requires working through six to seven interconnected representations for a single line.

Discuss with students why some chart cells are marked "Answers May Vary" (for example, when choosing two points on a line), so they understand multiple correct answers are possible rather than assuming they made an error.

Use Function I, "Create Your Own," as a formative check after the first eight functions, since it requires students to generate and represent a line themselves rather than transform a given one.

Form conversion — students rewrite a linear equation among standard form, slope-intercept form, and point-slope form starting from just one given form.

Slope and intercept identification — students determine a line's x-intercept, y-intercept, and slope from whichever representation is provided.

Graphing and tabulating — students build a table of values and plot a graph consistent with the function's equation.

Function construction — in the "Create Your Own" chart, students invent a linear function and represent it across every format themselves.