Creating and Graphing Two Variable Equations - Algebra 2
Card 1 of 30
Identify the $y$-intercept of $y=-2x+6$.
Identify the $y$-intercept of $y=-2x+6$.
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$y=6$. Set $x=0$: $y=-2(0)+6=6$.
$y=6$. Set $x=0$: $y=-2(0)+6=6$.
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Identify the correct scale choice if $x$ values run from $0$ to $200$ on a $10$-tick axis.
Identify the correct scale choice if $x$ values run from $0$ to $200$ on a $10$-tick axis.
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$20$ units per tick. Divide total range by number of intervals: $\frac{200}{10}=20$.
$20$ units per tick. Divide total range by number of intervals: $\frac{200}{10}=20$.
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What is the equation stating that $y$ is $n$ times $x$?
What is the equation stating that $y$ is $n$ times $x$?
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$y=nx$. One quantity is a multiple of another.
$y=nx$. One quantity is a multiple of another.
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What is the equation for distance $d$ at constant speed $r$ over time $t$?
What is the equation for distance $d$ at constant speed $r$ over time $t$?
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$d=rt$. Distance equals rate times time for uniform motion.
$d=rt$. Distance equals rate times time for uniform motion.
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Identify the slope of the line given by $3x-2y=8$.
Identify the slope of the line given by $3x-2y=8$.
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$m=\frac{3}{2}$. Rewrite $3x-2y=8$ as $y=\frac{3}{2}x-4$ to find slope.
$m=\frac{3}{2}$. Rewrite $3x-2y=8$ as $y=\frac{3}{2}x-4$ to find slope.
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What is the equation for converting Celsius $C$ to Fahrenheit $F$?
What is the equation for converting Celsius $C$ to Fahrenheit $F$?
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$F=\frac{9}{5}C+32$. Temperature conversion from Celsius to Fahrenheit scale.
$F=\frac{9}{5}C+32$. Temperature conversion from Celsius to Fahrenheit scale.
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What is the equation for converting Fahrenheit $F$ to Celsius $C$?
What is the equation for converting Fahrenheit $F$ to Celsius $C$?
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$C=\frac{5}{9}(F-32)$. Temperature conversion from Fahrenheit to Celsius scale.
$C=\frac{5}{9}(F-32)$. Temperature conversion from Fahrenheit to Celsius scale.
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What is the equation stating that $y$ is $\frac{1}{n}$ of $x$?
What is the equation stating that $y$ is $\frac{1}{n}$ of $x$?
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$y=\frac{x}{n}$. One quantity is a fraction of another.
$y=\frac{x}{n}$. One quantity is a fraction of another.
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What is the equation stating that $y$ is $n$ less than $x$?
What is the equation stating that $y$ is $n$ less than $x$?
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$y=x-n$. One quantity is smaller than another by amount $n$.
$y=x-n$. One quantity is smaller than another by amount $n$.
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What is the equation stating that $y$ is $n$ more than $x$?
What is the equation stating that $y$ is $n$ more than $x$?
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$y=x+n$. One quantity exceeds another by amount $n$.
$y=x+n$. One quantity exceeds another by amount $n$.
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What is the equation for the sum of two numbers $x$ and $y$ being $S$?
What is the equation for the sum of two numbers $x$ and $y$ being $S$?
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$x+y=S$. Two quantities add up to a given total $S$.
$x+y=S$. Two quantities add up to a given total $S$.
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What is the equation for profit $P$ in terms of revenue $R$ and cost $C$?
What is the equation for profit $P$ in terms of revenue $R$ and cost $C$?
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$P=R-C$. Profit is revenue minus total costs.
$P=R-C$. Profit is revenue minus total costs.
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What is the equation for revenue $R$ when price per unit is $p$ and units sold is $x$?
What is the equation for revenue $R$ when price per unit is $p$ and units sold is $x$?
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$R=px$. Revenue equals price per unit times number of units sold.
$R=px$. Revenue equals price per unit times number of units sold.
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What is the equation for total cost $C$ with fixed fee $f$ and per-unit cost $p$ for $x$ units?
What is the equation for total cost $C$ with fixed fee $f$ and per-unit cost $p$ for $x$ units?
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$C=px+f$. Total cost includes fixed fee plus variable cost per unit.
$C=px+f$. Total cost includes fixed fee plus variable cost per unit.
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What is the equation for simple interest $I$ with principal $P$, rate $r$, and time $t$?
What is the equation for simple interest $I$ with principal $P$, rate $r$, and time $t$?
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$I=Prt$. Interest equals principal times rate times time period.
$I=Prt$. Interest equals principal times rate times time period.
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What is the equation for distance $d$ at constant speed $r$ over time $t$?
What is the equation for distance $d$ at constant speed $r$ over time $t$?
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$d=rt$. Distance equals rate times time for uniform motion.
$d=rt$. Distance equals rate times time for uniform motion.
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What is the equation for area $A$ of a rectangle in terms of length $L$ and width $W$?
What is the equation for area $A$ of a rectangle in terms of length $L$ and width $W$?
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$A=LW$. Product of adjacent sides gives rectangular area.
$A=LW$. Product of adjacent sides gives rectangular area.
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What is the equation for perimeter $P$ of a rectangle with length $L$ and width $W$?
What is the equation for perimeter $P$ of a rectangle with length $L$ and width $W$?
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$P=2L+2W$. Sum of all four sides of a rectangle.
$P=2L+2W$. Sum of all four sides of a rectangle.
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What does it mean for an ordered pair $(x,y)$ to satisfy an equation in two variables?
What does it mean for an ordered pair $(x,y)$ to satisfy an equation in two variables?
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It makes the equation true when substituted. The coordinates produce a true statement when plugged in.
It makes the equation true when substituted. The coordinates produce a true statement when plugged in.
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What is the equation of a line with slope $m$ passing through the origin?
What is the equation of a line with slope $m$ passing through the origin?
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$y=mx$. Line through origin with slope $m$ and $y$-intercept $0$.
$y=mx$. Line through origin with slope $m$ and $y$-intercept $0$.
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What is the meaning of the $y$-intercept of a graph in terms of solutions?
What is the meaning of the $y$-intercept of a graph in terms of solutions?
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The $y$-value where $x=0$. Point where graph crosses vertical axis.
The $y$-value where $x=0$. Point where graph crosses vertical axis.
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What is the meaning of the $x$-intercept of a graph in terms of solutions?
What is the meaning of the $x$-intercept of a graph in terms of solutions?
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The $x$-value where $y=0$. Point where graph crosses horizontal axis.
The $x$-value where $y=0$. Point where graph crosses horizontal axis.
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What is the equation for combined variation where $y$ varies directly with $x$ and inversely with $z$?
What is the equation for combined variation where $y$ varies directly with $x$ and inversely with $z$?
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$y=\frac{kx}{z}$. One variable proportional to quotient of two others.
$y=\frac{kx}{z}$. One variable proportional to quotient of two others.
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What is the equation for joint variation where $y$ varies jointly with $x$ and $z$?
What is the equation for joint variation where $y$ varies jointly with $x$ and $z$?
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$y=kxz$. One variable proportional to product of two others.
$y=kxz$. One variable proportional to product of two others.
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What is the equation for inverse variation between $y$ and $x$ with constant $k$?
What is the equation for inverse variation between $y$ and $x$ with constant $k$?
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$y=\frac{k}{x}$. Product $xy$ remains constant as one increases, other decreases.
$y=\frac{k}{x}$. Product $xy$ remains constant as one increases, other decreases.
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What is the equation for direct variation between $y$ and $x$ with constant $k$?
What is the equation for direct variation between $y$ and $x$ with constant $k$?
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$y=kx$. Linear relationship through origin with constant ratio $k$.
$y=kx$. Linear relationship through origin with constant ratio $k$.
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What is the equation of a vertical line passing through $x=h$?
What is the equation of a vertical line passing through $x=h$?
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$x=h$. All points have the same $x$-coordinate $h$.
$x=h$. All points have the same $x$-coordinate $h$.
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What is the equation of a horizontal line passing through $y=k$?
What is the equation of a horizontal line passing through $y=k$?
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$y=k$. All points have the same $y$-coordinate $k$.
$y=k$. All points have the same $y$-coordinate $k$.
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What is the slope formula using two points $(x_1,y_1)$ and $(x_2,y_2)$?
What is the slope formula using two points $(x_1,y_1)$ and $(x_2,y_2)$?
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$m= rac{y_2-y_1}{x_2-x_1}$. Rise over run between any two distinct points on a line.
$m= rac{y_2-y_1}{x_2-x_1}$. Rise over run between any two distinct points on a line.
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What is the standard form of a parabola that opens left or right with vertex $(h,k)$?
What is the standard form of a parabola that opens left or right with vertex $(h,k)$?
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$x=a(y-k)^2+h$. Horizontal parabola with vertex $(h,k)$ and parameter $a$.
$x=a(y-k)^2+h$. Horizontal parabola with vertex $(h,k)$ and parameter $a$.
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