Unit 3: Linear Equations and Graphs
A coordinate plane turns an equation into a picture -- every point on the line is a solution, and the line's steepness is its slope.
6 topics · 24 questions
Each topic is a path, not a menu: work down it in order and every question builds on the one above. Click any of them to watch the answer draw itself.
The Coordinate Plane and Plotting Points
- How it worksHow do the x-coordinate and y-coordinate tell you which direction to move from the origin?
- Worked exampleShow me where the point (-3, 4) lands on the coordinate plane and which quadrant it falls in.
- Common mistakeWhy doesn't the point (2, 5) land in the same spot as the point (5, 2)?
- Going furtherWhat happens to a point's location when you flip the signs of both its coordinates?
Your turn1 of 2
In which quadrant does the point (-3, 6) lie, where -3 is negative and 6 is positive?What the Graph of an Equation Actually Means
- How it worksHow does testing a point's coordinates in an equation prove whether that point sits on the line?
- Worked exampleShow me whether the point (3, 7) lies on the line y = 2x + 1.
- Common mistakeWhy doesn't a point that's close to the line count as being on the line?
- Going furtherWhat happens to the picture of an equation's solutions once you allow x to be any real number instead of just whole numbers?
Your turn1 of 2
Does the point (4, 36) lie on the line y = 4x + 8, given that 4·4 + 8 does not equal 36?Graphing a Line by Plotting Points
- How it worksHow do you build a table of x and y values and turn it into a graphed line?
- Worked exampleGraph the line y = -2x + 3 by plotting three points from a table of values.
- Common mistakeWhy doesn't a third plotted point ever land off the line if the first two points were correct?
- Going furtherWhat happens to a graphed line's points when every y-value in its table is doubled?
Your turn1 of 2
For the line y = -3x + 6, find the y-value in the table when x = 6.x- and y-Intercepts
- How it worksHow does setting y to zero find where a line crosses the x-axis?
- Worked exampleFind the x-intercept and y-intercept of the line 2x + 3y = 12.
- Common mistakeWhy isn't the y-intercept just whatever number happens to be at the end of an equation written in any form?
- Going furtherWhat happens to a line's intercepts when the whole equation is multiplied by a constant?
Your turn1 of 2
Find the x-intercept of the line 7x + 7y = 57.Slope as Steepness
- How it worksHow does rise over run turn the steepness you see into one number?
- Worked exampleFind the slope of the line through the points (1, 2) and (4, 11).
- Common mistakeWhy doesn't a negative slope mean a line is less steep than a positive one?
- Going furtherWhat happens to a line's slope value as the line gets closer and closer to vertical?
- Going furtherWhat does it mean for a line to have a slope of exactly zero?
Your turn1 of 2
Find the slope of the line through the points (3, 6) and (9, 16).Rate of Change from a Table
- How it worksHow does dividing the change in y by the change in x from two table rows give you the rate of change?
- Worked exampleFind the rate of change shown in a table where x goes 2, 4, 6 and y goes 9, 15, 21.
- Common mistakeWhy doesn't a table with unevenly spaced x-values let you find slope by just subtracting neighboring y-values?
Your turn1 of 2
A table shows x going 2, 5, 9 and y going 3, 16, 33, evenly spaced. Find the rate of change.