Task Sets: Create equations in two or more variables - Common Core Math - HS Algebra

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Warm-Up: Review What You Know

These problems review skills you have already learned.

Which ordered pair is a solution to $y = 4x - 3$ ?

$(0, 3)$

$(2, 5)$

$(1, 0)$

$(-1, 7)$

A car travels at a constant speed of 55 miles per hour. Which equation gives the distance $d$ (in miles) after $t$ hours?

$d = 55 + t$

$t = 55d$

$d = 55t$

$d = \frac{t}{55}$

A graph shows hours worked ( $h$ ) on the horizontal axis and total pay in dollars ( $P$ ) on the vertical axis. Which statement correctly explains the axis assignment?

It is wrong — $P$ should be on the horizontal axis because pay is more important.

It is correct — $h$ is the independent variable (input) and $P$ depends on it.

It does not matter which variable goes on which axis.

It is wrong — both variables should share the same axis.

Fluency Practice

A phone plan charges a flat fee of $25 per month plus $0.10 per text message. Write the equation for monthly cost $C$ (in dollars) in terms of the number of texts $n$ , then find the monthly cost when $n = 80$ . Enter the cost in dollars.

A tank holds 400 liters of water and drains at 15 liters per minute. The volume remaining after $t$ minutes is $V = 400 - 15t$ . What is $V$ when $t = 12$ ? Enter your answer in liters.

A fruit stand sells pears for $1.50 each and bunches of grapes for $2.00 each. A customer spends exactly $12. Let $p$ = pears and $g$ = grape bunches. Which equation represents all valid spending combinations?

$1.50p + 2.00g = 12$

$p + g = 12$

$2.00p + 1.50g = 12$

$1.50p \cdot 2.00g = 12$

$Line y = -2x + 8 from (0,8) to (4,0) with four labeled candidate points A through D$

The line $y = -2x + 8$ is graphed on axes with $x$ from 0 to 4 and $y$ from 0 to 8. Which ordered pair lies on this line?

$(1, 4)$

$(2, 4)$

$(3, 3)$

$(1, 7)$

A ball drops from rest and its height $h$ (feet) after $t$ seconds is $h = 100 - 16t^2$ . What type of equation is this and what shape is its graph?

Linear — a straight line

Exponential — a J-shaped curve

Quadratic — a parabola

Absolute value — a V-shape

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Exercises: Creating and Graphing Two-Variable Equations

Warm-Up: Review What You Know

Fluency Practice