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: What is the slope of the line through $(1,2)$ and $(5,10)$?

Answer: $m=2$. Use slope formula: $m=\frac{10-2}{5-1}=\frac{8}{4}=2$.

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

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

Flashcard 3: What is the equation for density $D$ given mass $m$ and volume $V$?

Answer: $D=\frac{m}{V}$. Density equals mass per unit volume.

Flashcard 4: What is the slope-intercept form of a line in two variables?

Answer: $y=mx+b$. Where $m$ is slope and $b$ is the $y$-intercept.

Flashcard 5: What is the equation of the line through $(2,5)$ with slope $-3$?

Answer: $y-5=-3(x-2)$. Point-slope form using given point and slope.

Flashcard 6: What is the general form of a linear equation in two variables?

Answer: $Ax+By=C$. Standard form where $A$, $B$, $C$ are constants and $A$, $B$ not both zero.

Flashcard 7: 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 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 $n$ times $x$?

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

Flashcard 10: What is the equation representing that the perimeter is $24$ for a rectangle with sides $x$ and $y$?

Answer: $2x+2y=24$. Perimeter formula $P=2x+2y$ set equal to $24$.

Flashcard 11: What is the equation for average speed $v$ given distance $d$ and time $t$?

Answer: $v=\frac{d}{t}$. Speed equals distance divided by time elapsed.

Flashcard 12: What is the equation of the circle centered at $(2,-1)$ with radius $3$?

Answer: $(x-2)^2+(y+1)^2=9$. Standard circle form with center $(2,-1)$ and radius $3$.

Flashcard 13: What is the equation of a horizontal line passing through $y=k$?

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

Flashcard 14: What is the point-slope form of a line through $(x_1,y_1)$ with slope $m$?

Answer: $y-y_1=m(x-x_1)$. Uses a known point and slope to define the line.

Flashcard 15: 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 16: What is the standard form of a parabola that opens up or down with vertex $(h,k)$?

Answer: $y=a(x-h)^2+k$. Vertex form where $a$ determines width and direction of opening.

Flashcard 17: 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 18: What is the equation of the line through $(0,-2)$ and $(3,4)$?

Answer: $y=2x-2$. Slope is $\frac{4-(-2)}{3-0}=2$, use point-slope form.

Flashcard 19: 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 20: 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 21: What is the equation for remaining money $R$ after spending $s$ from an initial $50$?

Answer: $R=50-s$. Remaining amount decreases linearly with spending.

Flashcard 22: 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 23: What is the equation of the line with slope $4$ and $y$-intercept $-3$?

Answer: $y=4x-3$. Direct substitution into slope-intercept form $y=mx+b$.

Flashcard 24: 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 25: 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 26: Identify the $y$-intercept of the line given by $3x-2y=8$.

Answer: $b=-4$. From slope-intercept form $y=\frac{3}{2}x-4$, $y$-intercept is $-4$.

Flashcard 27: What is the equation stating that $y$ is $n$ more than $x$?

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

Flashcard 28: What is the equation for total pay with hourly wage $15$ for $h$ hours plus bonus $20$?

Answer: $P=15h+20$. Linear pay function with hourly rate plus fixed bonus.

Flashcard 29: What is the equation of a vertical line passing through $x=h$?

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

Flashcard 30: What is the equation of the horizontal line through $(7,-4)$?

Answer: $y=-4$. Horizontal lines have constant $y$-value.

Flashcard 31: 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 32: 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 33: What is the equation of the vertical line through $(-3,8)$?

Answer: $x=-3$. Vertical lines have constant $x$-value.

Flashcard 34: 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 35: What is the equation representing that $y$ varies directly with $x$ and $y=12$ when $x=3$?

Answer: $y=4x$. Find $k$ using $12=4(3)$, so $k=4$.

Flashcard 36: 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 37: 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 $a$.

Flashcard 38: What is the equation for a taxi fare with base fee $3$ and $2$ dollars per mile $m$?

Answer: $C=2m+3$. Linear cost function with fixed base fee and variable rate.

Flashcard 39: Identify the equation representing that the sum of angles $x$ and $y$ is $180$.

Answer: $x+y=180$. Two angles that sum to $180$ degrees are supplementary.

Flashcard 40: 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 41: What is the equation representing inverse variation if $y=5$ when $x=2$?

Answer: $y=\frac{10}{x}$. Find $k$ using $5=\frac{k}{2}$, so $k=10$.

Flashcard 42: Identify the $x$-intercept of $y=-2x+6$.

Answer: $x=3$. Set $y=0$ and solve: $0=-2x+6$, so $x=3$.

Flashcard 43: 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 44: 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 45: What is the equation representing that the area is $30$ for a rectangle with sides $x$ and $y$?

Answer: $xy=30$. Area formula $A=xy$ set equal to $30$.

Flashcard 46: 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 47: What is the equation of the parabola with vertex $(1,-4)$ and $a=2$ opening upward?

Answer: $y=2(x-1)^2-4$. Vertex form with $(h,k)=(1,-4)$ and $a=2$.

Flashcard 48: 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 49: What is the standard form of a circle with center $(h,k)$ and radius $r$?

Answer: $(x-h)^2+(y-k)^2=r^2$. Distance from center $(h,k)$ to any point on circle equals $r$.

Flashcard 50: 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 51: 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 52: 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 53: 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 54: 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 55: What is the equation of the parabola with vertex $(1,-4)$ and $a=2$ opening upward?

Answer: $y=2(x-1)^2-4$. Vertex form with $(h,k)=(1,-4)$ and $a=2$.