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MA.912.A.3.10 Writing Equations of Lines and Inequalities

What You Need To Know...

Write an equation of a line or an inequality  with given information.

  1. The benchmark will be assessed using MC (Multiple Choice) and FR (Fill in Response) items.
  2. Items may give two points on a line, a point and the slope of a line, or its graph.
  3. Items may require the use of coordinate geometry to find slopes, parallel lines, perpendicular lines, and equations of lines.
  4. Information given to determine equations of lines may include a table of values, the x- and y-intercepts, two points, the slope and a point, a graph, or an equation.
  5. Equations of lines may be represented in standard, slope-intercept, or point-slope form.
  6. Items may require students to rewrite equations of lines from standard form to slope-intercept form, and vice versa.
  7. Items may require students to identify a linear inequality in slope-intercept form.
  8. Fill-in response items may require that students provide a slope of a line parallel or perpendicular to a given line.  

Example One

In a technical drawing class, students are analyzing the side view of a house that has been positioned on a coordinate grid, as shown below.




Which of the following equations best represents the line that contains  PQ.jpg ?





Example Two

On the coordinate grid below, line l is perpendicular to  AB.jpg.




What is the slope of line l ?

Answer grid.jpg



Example Three

The line AB is graphed on the coordinate grid below.


What is the x-intercept of the line that is perpendicular to line AB at point B?



Additional Examples


Given a Graph

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Given Two Points

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Slope-Intercept Form

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Point-Slope Form

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Standard Form

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Parallel & Perpendicular

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Parallel Lines

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Perpendicular Lines

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Reference Sheet