Writing Linear Functions
Lessons in this chapter
About Writing Linear Functions
Writing Linear Functions covers every common way to construct a line’s equation, then extends linear thinking to sequences and piecewise-defined functions.
Writing Equations in Slope-Intercept Form and Writing Equations in Point-Slope Form cover writing a line's equation from a slope and one point, while Writing Equations of Parallel and Perpendicular Lines uses the relationship between slopes (equal for parallel lines, negative reciprocals for perpendicular lines) to write a new line's equation relative to a given one.
Scatter Plots and Lines of Fit and Analyzing Lines of Fit apply line-writing skills to real, imperfectly-linear data, drawing and then using a best-fit line to make predictions and judge how well it actually fits.
Arithmetic Sequences treats a sequence with a constant difference between terms as a linear function of its position number, and Piecewise Functions closes the chapter by defining a function using different linear (or other) rules over different intervals of its domain.
The seven lessons in this chapter each open as an Algebra 1 worksheet in the page, from Writing Equations in Point-Slope Form through Scatter Plots and Lines of Fit, Arithmetic Sequences and Piecewise Functions. Every question is marked as you answer it, so you can see immediately whether a perpendicular slope has been taken as the negative reciprocal or just the negative. All seven are free to try, with no login needed for your first 3.
Frequently asked questions
Writing Equations in Slope-Intercept Form and Writing Equations in Point-Slope Form build a line's equation from the information a problem actually gives, and Writing Equations of Parallel and Perpendicular Lines uses equal and negative reciprocal slopes. Scatter Plots and Lines of Fit and Analyzing Lines of Fit move to real data, fitting a line and judging how well it describes the points, before Arithmetic Sequences treats a constant step as a linear rule and Piecewise Functions lets different rules apply over different intervals. The chapter sits mainly in the high school Functions conceptual category (F), with the two lines of fit lessons in Statistics and Probability (S).
Use point-slope form, y - y₁ = m(x - x₁), substituting the known slope and point, then simplify into slope-intercept form if needed.
Calculate the slope from the two points first (rise over run), then use point-slope form with either point to find the full equation.
Parallel lines have the exact same slope, so use the given line’s slope with the new point (via point-slope form) to write the parallel line’s equation.
Perpendicular lines have slopes that are negative reciprocals of each other: flip the given slope and change its sign, then use that new slope with the new point.
A line of best fit is a single straight line that best approximates the overall trend in scattered data, not a line that passes through every point exactly: it's meant to summarize a pattern, not trace it precisely.