Coordinate Plane & Graphing Lines
Key vocabulary and skills for plotting points, finding slope, and graphing linear equations.
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Questions Covered in This Set
11 cards to master
What is the origin, and how is it written?
The point where the x-axis and y-axis cross, written (0, 0).
In an ordered pair (x, y), what does each number tell you?
x is the horizontal move (right/left), y is the vertical move (up/down) — 'down the hall, then up the stairs.'
State the slope formula.
m = (y₂ − y₁)/(x₂ − x₁) = rise/run
Find the slope through (−2, 5) and (3, −5).
m = (−5 − 5)/(3 − (−2)) = −10/5 = −2 (down 2 for every 1 right).
What kind of line has zero slope? Undefined slope?
Zero slope = horizontal line, y = c. Undefined slope = vertical line, x = c (run is 0, can't divide by zero).
In y = mx + b, what are m and b?
m is the slope; b is the y-intercept, the point (0, b) where the line crosses the y-axis.
How do you graph y = (2/3)x − 4?
Plot (0, −4), then go up 2, right 3 to (3, −2), again to (6, 0), and draw the line.
Fastest way to graph Ax + By = C?
Find intercepts: set x = 0 to get the y-intercept, set y = 0 to get the x-intercept, then connect the two points.
Shortcut for the slope of Ax + By = C?
Slope = −A/B (e.g., 3x + 4y = 12 has slope −3/4).
How do slopes of parallel vs. perpendicular lines compare?
Parallel lines have equal slopes; perpendicular slopes are negative reciprocals whose product is −1.
How do you test whether a point lies on a line?
Substitute the coordinates into the equation; if both sides are equal, the point is on the line.
