Card 1 of 20
EasyStudy card 1
Prompt
What is average rate of change?
Output change per input change.
Answer
Change in the dependent variable divided by change in the independent variable.
Example
\(\Delta y/\Delta x\).
MathChapter 3: Functions and Linear Equations
Flashcards
Rate of Change and Slope Flashcards
Twenty original recall cards covering 3-2 rate of change and slope concepts, procedures, graphs, and traps.
Current card1 / 20
Session progress0 of 20 studied
Card 1 of 20. Answer hidden.
Card 2 of 20
EasyStudy card 2
Prompt
State the slope formula.
Subtract in matching order.
Answer
\(m=(y_2-y_1)/(x_2-x_1)\).
Example
Reverse both differences and the slope stays the same.
Card 3 of 20
EasyStudy card 3
Prompt
What is rise?
Numerator of slope.
Answer
The vertical change \(\Delta y\).
Example
Rise \(=y_2-y_1\).
Card 4 of 20
EasyStudy card 4
Prompt
What is run?
Denominator of slope.
Answer
The horizontal change \(\Delta x\).
Example
Run \(=x_2-x_1\).
Card 5 of 20
EasyStudy card 5
Prompt
How does a positive-slope line move left to right?
y increases as x increases.
Answer
It rises.
Example
Slope \(3/4\) is positive.
Card 6 of 20
EasyStudy card 6
Prompt
How does a negative-slope line move left to right?
y decreases as x increases.
Answer
It falls.
Example
Slope \(-2\) is negative.
Card 7 of 20
MediumStudy card 7
Prompt
What is the slope of a horizontal line?
The run may be nonzero.
Answer
Zero, because its rise is zero.
Example
\(y=5\) has slope \(0\).
Card 8 of 20
MediumStudy card 8
Prompt
What is the slope of a vertical line?
Division by zero is undefined.
Answer
Undefined, because its run is zero.
Example
\(x=-1\) has undefined slope.
Card 9 of 20
MediumStudy card 9
Prompt
Why must coordinate subtraction order match?
Reverse both or neither.
Answer
Reversing only one difference changes the sign incorrectly.
Example
\((5-1)/(4-2))=((1-5)/(2-4))\).
Card 10 of 20
MediumStudy card 10
Prompt
What units should a slope have?
Read y per x.
Answer
Dependent-variable units per independent-variable unit.
Example
Dollars per hour, not hours per dollar.
Card 11 of 20
MediumStudy card 11
Prompt
How does a table show linearity?
Input steps need not be equal.
Answer
The ratio \(\Delta y/\Delta x\) stays constant across intervals.
Example
Compare at least two intervals.
Card 12 of 20
MediumStudy card 12
Prompt
How do you find the x-intercept of Ax + By = C?
An x-axis point has y zero.
Answer
Set \(y=0\) and solve for x.
Example
Its point form is \((x,0)\).
Card 13 of 20
MediumStudy card 13
Prompt
How do you find the y-intercept?
A y-axis point has x zero.
Answer
Set \(x=0\) and solve for y.
Example
Its point form is \((0,y)\).
Card 14 of 20
MediumStudy card 14
Prompt
What is a zero of a function?
It is an x-coordinate.
Answer
An input c for which \(f(c)=0\).
Example
Graphically it is an x-intercept.
Card 15 of 20
MediumStudy card 15
Prompt
Why is y/x not generally slope?
The origin is not automatically a point.
Answer
Slope compares changes, not raw coordinates.
Example
Use \((y_2-y_1)/(x_2-x_1)\).
Card 16 of 20
MediumStudy card 16
Prompt
What does a negative real-world slope mean?
Keep the sign in interpretation.
Answer
The dependent quantity decreases as the independent quantity increases.
Example
\(-8\) liters/minute means losing 8 liters each minute.
Card 17 of 20
MediumStudy card 17
Prompt
How can standard form reveal slope?
Isolate y.
Answer
Solve for y; in \(Ax+By=C\), slope is \(-A/B\) when \(B\ne0\).
Example
\(3x+2y=8\) has slope \(-3/2\).
Card 18 of 20
MediumStudy card 18
Prompt
How do you find a missing coordinate from a known slope?
Keep unknown inside the correct difference.
Answer
Write the coordinate slope expression, set it equal to the known slope, and solve.
Example
\((k-2)/(5-1))=3\).
Card 19 of 20
MediumStudy card 19
Prompt
What is the independent variable?
It drives the comparison.
Answer
The input or explanatory quantity, usually on the horizontal axis.
Example
Time is often independent.
Card 20 of 20
MediumStudy card 20
Prompt
What is the dependent variable?
Usually on the vertical axis.
Answer
The output quantity whose value responds to the independent variable.
Example
Distance may depend on time.
Deck complete
You rated every card. Revisit difficult cards or shuffle for another pass.
Keyboard: Space reveals, left/right arrows navigate, 1–4 rate, and S shuffles.