Unit 9: The Coordinate Plane and Linear Graphs
Plotting points in all four quadrants, reading slope as rise over run, and finding where two lines cross.
6 topics · 22 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 Its Four Quadrants
- How it worksHow do the signs of the x-coordinate and y-coordinate decide which of the four quadrants a point falls in?
- Worked exampleGraph the points negative 3 comma 4, and 5 comma negative 2, and name which quadrant each one is in.
- Common mistakeWhy doesn't the point 0 comma 5 sit inside any of the four quadrants?
Your turn1 of 2
Which quadrant contains the point negative 7 comma 7 (negative x, positive y)?Graphing Linear Relationships
- How it worksHow does plugging in several x values and plotting the resulting points reveal the line an equation describes?
- Worked exampleGraph y equals 2x plus 1 by plotting at least three points.
- Going furtherWhat happens to the graph of a line when you change its equation from y equals 2x plus 1 to y equals 2x minus 3?
Your turn1 of 2
A taxi ride costs 5 dollars to start plus 4 dollars per mile, x. Using the cost formula y equals 4x plus 5, find the total cost, y, when the ride is 9 miles.Slope as Rise Over Run
- How it worksHow do you count the rise and the run between two points on a line to find its slope?
- Worked exampleFind the slope of the line through the points 1 comma 2 and 4 comma 11.
- Going furtherWhat happens to a line's slope when the line tilts downward from left to right instead of upward?
- Common mistakeWhy isn't slope just the run over the rise, flipped upside down?
Your turn1 of 2
A ramp rises from the point (3, 6) to the point (12, 8) on a blueprint. What is its slope?Slope-Intercept Form
- How it worksHow do the m and the b in y equals mx plus b each control a different part of the line's picture?
- Worked exampleGraph y equals negative 3x plus 2 using its slope and y-intercept.
- Worked exampleFind the equation in slope-intercept form for a line with slope 4 that passes through 0 comma negative 5.
- Common mistakeWhy doesn't the y-intercept in y equals mx plus b tell you anything about how steep the line is?
- Ties togetherHow does slope-intercept form connect to the constant of proportionality you found for lines through the origin?
Your turn1 of 2
A savings account grows at a slope of 7 dollars per month and started at (0, 3), meaning 3 dollars. Find the balance, y, after 9 months.Interpreting a Graph's Story
- How it worksHow does the steepness and direction of a graph's segments translate into a story about speeding up, slowing down, or standing still?
- Worked exampleExplain the trip shown by a distance-time graph that rises steeply for 10 minutes, stays flat for 5 minutes, then rises gently for 15 minutes.
- Common mistakeWhy doesn't a graph that goes downhill mean the person is walking backward in time?
Your turn1 of 2
A distance-time graph rises steeply for 15 minutes, then goes flat for 11 minutes. What is happening during the flat part?Systems of Equations by Graphing
- How it worksHow does graphing two linear equations on the same plane reveal the single x and y that satisfy both?
- Worked exampleSolve the system y equals x plus 1 and y equals negative x plus 5 by graphing both lines.
- Common mistakeWhy doesn't a system of two equations always have exactly one solution?
- Going furtherWhat happens to the graph of a system when the two lines have the exact same slope?
Your turn1 of 2
Two hikers start walking toward each other: one's position is y equals x plus 7 and the other's is y equals negative x plus 23, where x is time in minutes. Solve the system to find the x-coordinate, in minutes, where they meet.