🧮 algebra

1. The problem is to verify if the equation manipulation from $2x + 3y = 12$ to $y = \frac{2}{3}x - 4$ is correct. 2. Start with the original equation:

1. **State the problem:** We need to graph the function $$y = -\left| \frac{1}{4}x \right| + 2$$ by transforming the parent absolute value function $$y = |x|$$.

1. The problem asks to complete the chart by finding the x-intercept, y-intercept, and slope-intercept form $y=mx+b$ for each equation. 2. Recall the intercepts:

1. **State the problem:** Simplify the expression $-2^4/4-4(12/6)+10$. 2. **Recall order of operations:** Exponents first, then multiplication and division from left to right, then

1. The problem is to convert the equation from standard form $3x - 2y = 6$ to slope-intercept form $y = mx + b$ and verify why the conversion is correct. 2. The standard form of a

1. **State the problem:** Simplify the expression $-2^4/4-4(48/6)+10$. 2. **Recall order of operations:** Exponents first, then multiplication and division from left to right, and

1. **State the problem:** We are given the system of equations: $$2x + 3y = 5$$

1. **State the problem:** Simplify the expression $$\left(\frac{2x^{3} y^{-3}}{3xy^{-2} \cdot 2y^{2}}\right)^{2}$$. 2. **Rewrite the denominator:** The denominator is a product: $$

1. The problem is to find the y-intercept $b$ in the linear equation $y = mx + b$ given a point and the slope. 2. The formula for a line is $y = mx + b$, where $m$ is the slope and

1. **State the problem:** We need to find the equation of line K that passes through the point $(15, 20)$ and is parallel to the line given by $$y = \frac{2}{5}x - 10.$$ 2. **Recal

1. **State the problem:** We want to find how much more expensive a pint of apple juice is per fluid ounce compared to a quart of apple juice. 2. **Given information:**

1. **State the problem:** Find the equation of line W that passes through the point $(2, 11)$ and is parallel to the line $y = 4x + 5$. 2. **Recall the formula:** The general form

1. The problem is to find the y-intercept $b$ of the line given the slope $m=3$ and a point on the line. 2. The equation of a line in slope-intercept form is:

1. **State the problem:** We want to find the slope $m$ of the line passing through the points $(2, -4)$ and $(5, 5)$. 2. **Formula for slope:** The slope $m$ between two points $(

1. **State the problem:** Solve the quadratic equation $$8)\ 2m^2 - 7m - 13 = -10$$. 2. **Rewrite the equation:** Move all terms to one side to set the equation equal to zero.

1. **State the problem:** We need to sketch the graph of a line with slope $2$ and y-intercept $3$. 2. **Recall the formula:** The equation of a line in slope-intercept form is $$y

1. The problem is to solve an equation using substitution method. 2. Substitution involves replacing a complicated expression with a simpler variable to make the equation easier to

1. **Stating the problem:** You want to solve a linear system where none of the variables have a coefficient of 1. 2. **General approach:** The goal is to isolate variables or elim

1. The problem is to find equivalent fractions for $\frac{5}{6}$ and $\frac{3}{4}$ using the least common denominator (LCD). 2. The LCD is the smallest number that both denominator

1. The problem asks for the least common denominator (LCD) of the fractions $\frac{3}{5}$ and $\frac{1}{10}$.\n\n2. The denominator is the bottom number of a fraction, and the LCD

1. **State the problem:** Solve the system of linear equations: $$\begin{cases} 3x - 2y = 5 \\ x - 4y - z = 7 \\ 14x - 6y + z = -13 \end{cases}$$