HSA.CED.A.2 Tutor Intake — Two-Variable Equations and Graphs

A one-variable equation like $40 + 25m = 215$ finds a specific value
of $m$. How is a two-variable equation like $C = 25m + 40$ different?

A tank holds 500 liters of water and drains at 20 liters per minute.
The equation is $V = 500 - 20t$, where $V$ is the volume (liters) and
$t$ is the time (minutes).

Which axis assignment is correct when graphing this equation?

A student graphs $V = 500 - 20t$ and marks only the points
$(0, 500)$, $(5, 400)$, $(10, 300)$, $(15, 200)$, $(20, 100)$,
and $(25, 0)$ as separate dots, leaving gaps between them.

Which statement best identifies the error?

A car gets 30 miles per gallon and starts with a full 12-gallon tank.

Let $d$ = miles driven and $g$ = gallons remaining.

The two-variable equation is $g = 12 - \frac{d}{30}$.

How many gallons remain after the car has traveled 90 miles? Enter a
number.

A ball is thrown upward from the ground with an initial velocity of
48 feet per second. Its height $h$ (feet) as a function of time $t$
(seconds) follows the quadratic pattern used in projectile motion.

Which equation correctly models this relationship?

A fruit stand sells apples for $1.50 each and oranges for $2.00 each.
The two-variable equation for spending exactly $12 is:

$1.50a + 2.00o = 12$

where $a$ = number of apples and $o$ = number of oranges.

If a customer buys 4 apples, how many oranges can they buy to spend
exactly $12?