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Geometry 3-7 Complete Lesson: Equations of Lines in the Coordinate Plane

By Matt Richardson
Last updated about 3 years ago
41 Questions
Note from the author:
A complete formative lesson with embedded slideshow, mini lecture screencasts, checks for understanding, practice items, mixed review, and reflection. I create these assignments to supplement each lesson of Pearson's Common Core Edition Algebra 1, Algebra 2, and Geometry courses. See also mathquest.net and twitter.com/mathquestEDU.

Solve It! Ski resorts use steepness to rate the difficulty of their hills. The steeper the hill, the higher the difficulty rating. Shown are stretches of three new hills at a particular resort.


Which hill gets which rating?

Hill A
Easiest
Hill B
Intermediate
Hill C
Difficult

Take Note: Define slope. You may use the canvas to help illustrate your description.

Take Note: Describe how you can find the slope of a line if you know the coordinates of two points on the line. You may use the canvas to help illustrate your description.

Problem 1 Got It? What is the slope of line a?

Problem 1 Got It? What is the slope of line c? Enter only a number.

Take Note: On the canvas, sketch an example of a line that has positive slope.

Take Note: On the canvas, sketch an example of a line that has negative slope.

Take Note: On the canvas, sketch an example of a line that has zero slope.

Take Note: On the canvas, sketch an example of a line that has undefined slope.

Take Note: Write the general equation for slope-intercept form. Enter only the equation, with no spaces.

Take Note: Write the general equation for point-slope form. Enter only the equation, with no spaces.
Hints: You may use the subscript button on the math input keyboard or the underscore key to initiate subscript. Use the right arrow to exit subscript.

Problem 2 Got It? Graph the equation on the canvas.
Be sure to include all relevant graph detail: label axes, indicate units on both axes, and use arrows to represent end behavior, as appropriate.

Problem 2 Got It? Graph the equation on the canvas.
Be sure to include all relevant graph detail: label axes, indicate units on both axes, and use arrows to represent end behavior, as appropriate.

Problem 2 Extension: Graph both equations on the same plane using the embedded Desmos utility. Zoom and pan your graph to establish an appropriate viewing window.

Problem 3 Got It?

Problem 3 Got It?

Take Note: Summarize the process of writing the equation of a line in slope-intercept form when you know the coordinates of two points on the line. You may use the canvas to help illustrate your description.

Take Note: Summarize the process of writing the equation of a line in point-slope form when you know the coordinates of two points on the line. You may use the canvas to help illustrate your description.

Problem 4 Got It? Graph both of the equations below, created from Problem 4 and its Got It, on the same plane. Zoom and pan your graph to establish an appropriate viewing window.

Take Note: Match each graph with its slope.

Positive slope
Negative slope
Zero slope
Undefined slope

Problem 5 Got It?

Problem 5 Got It?

What is an equation of a line with slope 8 and y-intercept 10?

Compare and Contrast: Graph the equations on the canvas.
Be sure to include relevant graph detail: label axes, indicate units on both axes, and use arrows to represent end behavior, as appropriate.

Error Analysis: A classmate found the slope of the line passing through (8, -2) and (8, 10), as shown here. Describe your classmate's error.

Find the correct slope of the line passing through the given points.

Review Lesson 2-5: Categorize each statement based on the property it demonstrates.

  • \overline{RS} \cong \overline{RS}
  • If \angle{1} \cong \angle{4}, then \angle{4} \cong \angle{1}.
  • 4(2a-3)=8a-12
  • If b+c=7 and b=2, then 2+c=7.
  • Symmetric property of congruence
  • Distributive property
  • Reflexive property of congruence
  • Substitution property of equality

Review Lesson 3-7: Find the slope of the line passing through the points.

Review Lesson 3-7: Find the slope of the line passing through the points.

Vocabulary Review: Categorize each statement on the left as true or false.

  • The ordered pair for the origin is (0, 0).
  • An ordered pair describes the location of a point in a coordinate grid.
  • An ordered pair can be written as (x-coordinate, y-coordinate) or (y-coordinate, x-coordinate).
  • True
  • False

Use Your Vocabulary: Complete each statement on the right with the appropriate word from the left. Use each word only once.

  • slope
  • sloped
  • sloping
  • The __?__ of the hill made it difficult for bike riding.
  • The driveway __?__ down to the garage.
  • The __?__ lawn led to the river.

Use Your Vocabulary: Match each word on the left with its part of speech on the right.

lining
ADJECTIVE
linear
NOUN
line
VERB (present-tense)

Reflection: Math Success