6.1-6.3 Test Review Flashcards

Vocabulary practice flashcards covering slope, rate of change, slope-intercept form, standard form, and finding intercepts based on the 6.1-6.3 Test Review notes.

Rate of Change (Time vs. Money Table)

Calculated as $\frac{\Delta y}{\Delta x} = \frac{60}{3} = \frac{20}{1}$, which means making $\\n20$ for every $1\,\text{hour}$ of work.

Rate of Change (Battery Capacity Graph)

Calculated as $\frac{10}{5} = \frac{2}{1}$, which means the battery charge increases by $2\%$ every $1\,\text{minute}$.

Slope Formula

$$m = \frac{y_2 - y_1}{x_2 - x_1}$$

Slope Between Points $(2, 5)$ and $(4, 11)$

$$m = \frac{11 - 5}{4 - 2} = \frac{6}{2} = 3$$

Slope of a Horizontal Line

The slope of any horizontal line is $0$.

Slope-Intercept Form

$y = mx + b$, where $m$ represents the slope and $b$ represents the y-intercept.

Slope and y-intercept of $y = -5x + 3$

The slope is $m = -5$ and the y-intercept is $b = 3$.

Equation of Line with Slope $m = \frac{1}{2}$ and y-intercept $b = 2$

$$y = \frac{1}{2}x + 2$$

x-intercept and y-intercept of $4y + 3x = 12$

The x-intercept is $4$ (from $3x = 12$) and the y-intercept is $3$ (from $4y = 12$).

Standard Form of a Linear Equation

$Ax + By = C$, where $A$, $B$, and $C$ are written using integers.

Standard Form of $y = -\frac{2}{5}x + 4$

$5y + 2x = 20$ (or $2x + 5y = 20$), obtained by multiplying all terms by $5$ and adding $2x$ to both sides.

Standard Form Linear Equation for Candy Store Purchase

$3.25j + 1.75s = 25$, where $j$ represents pounds of Jolly Ranchers at $\\n3.25$ per pound and $s$ represents pounds of Smarties at $\\n1.75$ per pound for a total of $\\n25$.

Intercepts of $-x + 2y = 6$

The x-intercept is $(-6, 0)$ (from $-1x = 6$) and the y-intercept is $(0, 3)$ (from $2y = 6$).

Points on the Horizontal Line $y = -3$

Any ordered pairs where the y-coordinate is $-3$, such as $(0, -3)$, $(2, -3)$, and $(-4, -3)$.