🧮 algebra

1. **State the problem:** We need to find the slope $m$ of the line passing through the points $(4,-2)$ and $(3,3)$. 2. **Formula for slope:** The slope $m$ between two points $(x_

1. **State the problem:** We need to find the slope $m$ of the line passing through the points $(-2,9)$ and $(3,-11)$. 2. **Formula for slope:** The slope $m$ between two points $(

1. **Problem statement:** We start with the line $y = x$ and transform it into the line $y = 2x + 4$. We need to find the slope and y-intercept of the new line, describe how the sl

1. **State the problem:** We are given the linear function $y = 2x + 4$ and want to analyze it. 2. **Formula and rules:** This is a linear equation in slope-intercept form $y = mx

1. **State the problem:** We start with the line $y = x$ and transform it into $y = 3x + 6$. We need to find the slope and y-intercept of the new line, describe how the slope chang

1. **State the problem:** We are given the linear function $y = -\frac{2}{3}x$ and want to understand its properties. 2. **Formula and explanation:** This is a linear function of t

1. The problem is to graph the direct variation equation $y = -\frac{2}{5}x$. 2. A direct variation equation has the form $y = kx$, where $k$ is the constant of variation.

1. The problem is to understand or analyze the function $f_1[x]$. 2. Typically, $f_1[x]$ denotes a function named $f_1$ with variable $x$.

1. **State the problem:** We know that $y$ varies directly with $x$, which means $y = kx$ for some constant $k$. 2. **Use the given values to find $k$:** Given $y = 77$ when $x = 7

1. **State the problem:** Calculate $6$ raised to the power of $3$, which means finding $6^3$. 2. **Formula:** The expression $a^b$ means multiplying $a$ by itself $b$ times. So, $

1. **State the problem:** Solve the system of equations: $$\frac{x}{y+7} = \frac{3}{7}$$

1. **State the problem:** We are given the equation $$(2x + 3y)^2 - 8x - 12y + 16 = 0$$ and need to find the value of $$A$$ where $$A = 2x + 3y$$. 2. **Rewrite the problem in terms

1. **State the problem:** The value of $y$ varies directly with $x$, and we know $y = -16$ when $x = 4$. We need to find $y$ when $x = 12$. 2. **Formula for direct variation:** Whe

1. **State the problem:** We are given the equation $X + 3 = y$ and need to solve for $X$. 2. **Formula and rules:** To isolate $X$, we use the rule of inverse operations. Since $3

1. **State the problem:** Solve the equation $\frac{x}{y+7} = \frac{3}{7}$ for $x$ in terms of $y$. 2. **Formula and rules:** When two fractions are equal, their cross products are

1. The problem is incomplete as it only states "If x, y satisfy:" without providing an equation or condition. 2. To solve or analyze a problem involving variables x and y, we need

1. **State the problem:** Find the slope of the line passing through the points $(2,3)$ and $(9,7)$. 2. **Formula for slope:** The slope $m$ between two points $(x_1,y_1)$ and $(x_

1. **State the problem:** Find the slope of the line passing through the points $(1,9)$ and $(4,4)$. 2. **Formula for slope:** The slope $m$ between two points $(x_1,y_1)$ and $(x_

1. **Stating the problem:** Solve the equation $$2x^2 - 5x + 3 = 0$$ for $x$. 2. **Formula used:** For quadratic equations of the form $$ax^2 + bx + c = 0$$, the solutions are give

1. **State the problem:** We are given data points with $x = 0, 3, 6, 9, 12$ and corresponding $y = 9, 8, 7, 6, 5$. We need to find the rate of change represented by this data. 2.

1. **State the problem:** We are given data points with $x = -7, 0, 7, 14, 21$ and corresponding $y = -1, 2, 5, 8, 11$. We need to find the rate of change represented by this data.