Algebra 2 Flashcards: Creating And Graphing Two Variable Equations

What this deck covers

This deck focuses on Creating And Graphing Two Variable Equations, giving you a quick way to review the definitions, rules, and examples that matter most for Algebra 2.

How to use these flashcards

Work through these flashcards in short sessions. Try to answer each prompt before flipping the card, then revisit any cards you miss until the explanation feels automatic.

Flashcard 1: Identify the $y$-intercept of $y=-2x+6$.

Answer: $y=6$. Set $x=0$: $y=-2(0)+6=6$.

Flashcard 2: Identify the correct scale choice if $x$ values run from $0$ to $200$ on a $10$-tick axis.

Answer: $20$ units per tick. Divide total range by number of intervals: $\frac{200}{10}=20$.

Flashcard 3: What is the equation stating that $y$ is $n$ times $x$?

Answer: $y=nx$. One quantity is a multiple of another.

Flashcard 4: What is the equation for distance $d$ at constant speed $r$ over time $t$?

Answer: $d=rt$. Distance equals rate times time for uniform motion.

Flashcard 5: Identify the slope of the line given by $3x-2y=8$.

Answer: $m=\frac{3}{2}$. Rewrite $3x-2y=8$ as $y=\frac{3}{2}x-4$ to find slope.

Flashcard 6: What is the equation for converting Celsius $C$ to Fahrenheit $F$?

Answer: $F=\frac{9}{5}C+32$. Temperature conversion from Celsius to Fahrenheit scale.

Flashcard 7: What is the equation for converting Fahrenheit $F$ to Celsius $C$?

Answer: $C=\frac{5}{9}(F-32)$. Temperature conversion from Fahrenheit to Celsius scale.

Flashcard 8: What is the equation stating that $y$ is $\frac{1}{n}$ of $x$?

Answer: $y=\frac{x}{n}$. One quantity is a fraction of another.

Flashcard 9: What is the equation stating that $y$ is $n$ less than $x$?

Answer: $y=x-n$. One quantity is smaller than another by amount $n$.

Flashcard 10: What is the equation stating that $y$ is $n$ more than $x$?

Answer: $y=x+n$. One quantity exceeds another by amount $n$.

Flashcard 11: What is the equation for the sum of two numbers $x$ and $y$ being $S$?

Answer: $x+y=S$. Two quantities add up to a given total $S$.

Flashcard 12: What is the equation for profit $P$ in terms of revenue $R$ and cost $C$?

Answer: $P=R-C$. Profit is revenue minus total costs.

Flashcard 13: What is the equation for revenue $R$ when price per unit is $p$ and units sold is $x$?

Answer: $R=px$. Revenue equals price per unit times number of units sold.

Flashcard 14: What is the equation for total cost $C$ with fixed fee $f$ and per-unit cost $p$ for $x$ units?

Answer: $C=px+f$. Total cost includes fixed fee plus variable cost per unit.

Flashcard 15: What is the equation for simple interest $I$ with principal $P$, rate $r$, and time $t$?

Answer: $I=Prt$. Interest equals principal times rate times time period.

Flashcard 16: What is the equation for distance $d$ at constant speed $r$ over time $t$?

Answer: $d=rt$. Distance equals rate times time for uniform motion.

Flashcard 17: What is the equation for area $A$ of a rectangle in terms of length $L$ and width $W$?

Answer: $A=LW$. Product of adjacent sides gives rectangular area.

Flashcard 18: What is the equation for perimeter $P$ of a rectangle with length $L$ and width $W$?

Answer: $P=2L+2W$. Sum of all four sides of a rectangle.

Flashcard 19: What does it mean for an ordered pair $(x,y)$ to satisfy an equation in two variables?

Answer: It makes the equation true when substituted. The coordinates produce a true statement when plugged in.

Flashcard 20: What is the equation of a line with slope $m$ passing through the origin?

Answer: $y=mx$. Line through origin with slope $m$ and $y$-intercept $0$.

Flashcard 21: What is the meaning of the $y$-intercept of a graph in terms of solutions?

Answer: The $y$-value where $x=0$. Point where graph crosses vertical axis.

Flashcard 22: What is the meaning of the $x$-intercept of a graph in terms of solutions?

Answer: The $x$-value where $y=0$. Point where graph crosses horizontal axis.

Flashcard 23: What is the equation for combined variation where $y$ varies directly with $x$ and inversely with $z$?

Answer: $y=\frac{kx}{z}$. One variable proportional to quotient of two others.

Flashcard 24: What is the equation for joint variation where $y$ varies jointly with $x$ and $z$?

Answer: $y=kxz$. One variable proportional to product of two others.

Flashcard 25: What is the equation for inverse variation between $y$ and $x$ with constant $k$?

Answer: $y=\frac{k}{x}$. Product $xy$ remains constant as one increases, other decreases.

Flashcard 26: What is the equation for direct variation between $y$ and $x$ with constant $k$?

Answer: $y=kx$. Linear relationship through origin with constant ratio $k$.

Flashcard 27: What is the equation of a vertical line passing through $x=h$?

Answer: $x=h$. All points have the same $x$-coordinate $h$.

Flashcard 28: What is the equation of a horizontal line passing through $y=k$?

Answer: $y=k$. All points have the same $y$-coordinate $k$.

Flashcard 29: What is the slope formula using two points $(x_1,y_1)$ and $(x_2,y_2)$?

Answer: m=rac{y_2-y_1}{x_2-x_1}. Rise over run between any two distinct points on a line.

Flashcard 30: What is the standard form of a parabola that opens left or right with vertex $(h,k)$?

Answer: $x=a(y-k)^2+h$. Horizontal parabola with vertex $(h,k)$ and parameter $a$.