Algebra Practice: Rewriting Quotients, Linear Graphs, and Slope Match

Practice flashcards reviewing rewriting quotients, interpreting linear functions and graphs, and finding slopes and y-intercepts from standard form equations.

How can the quotient $\frac{4x - 10}{2}$ be rewritten as a difference?

$$2x - 5$$

How can the quotient $\frac{1 - 50x}{-2}$ be rewritten as a sum or difference?

$$-\frac{1}{2} + 25x$$

How can the quotient $\frac{5(x+10)}{25}$ be rewritten as a sum or difference?

$$\frac{1}{5}x + 2$$

In the equation $a = 450 - 20t$ describing water in a tank over time, what does the vertical intercept $(0, 450)$ represent?

It represents the starting amount of $450\,\text{gallons}$ of water in the tank.

In the equation $a = 450 - 20t$ describing water in a tank over time, what does the slope $-20$ represent?

It means the tank loses $20\,\text{gallons}$ of water per minute.

In the context of Beth Anne's purchases, what relationship does the equation $6x + 9y = 75$ describe?

It describes the relationship between pounds of almonds ($x$), pounds of figs ($y$), and the total dollar amount ($75$) spent on them.

How can you verify that a graph represents the equation $6x + 9y = 75$ if the numbers $6$, $9$, or $75$ are not directly visible on the graph?

Substitute two points from the graph into the equation to verify if they make the equation true.

What are the slope $m$ and y-intercept for the graph of $-4x + 3y = 3$?

Slope $m = \frac{4}{3}$ and y-intercept $(0, 1)$

What are the slope $m$ and y-intercept for the graph of $12x - 4y = 8$?

Slope $m = 3$ and y-intercept $(0, -2)$

What are the slope $m$ and y-intercept for the graph of $8x + 2y = 16$?

Slope $m = -4$ and y-intercept $(0, 8)$

What are the slope $m$ and y-intercept for the graph of $-x + 1\frac{1}{3}y = 1\frac{1}{3}$?

Slope $m = \frac{3}{4}$ and y-intercept $(0, 1)$

What are the slope $m$ and y-intercept for the graph of $-4x + 3y = -6$?

Slope $m = \frac{4}{3}$ and y-intercept $(0, -2)$