6x - 7y = -12
Understand the Problem
The question presents a linear equation with two variables, x and y. It appears to be asking for a solution or analysis of the equation, which typically involves finding values for x and y that satisfy the equation, or perhaps converting it to slope-intercept form.
Answer
The equation in slope-intercept form is $y = -\frac{A}{B}x + \frac{C}{B}$.
Answer for screen readers
The slope-intercept form of the linear equation is $y = -\frac{A}{B}x + \frac{C}{B}$.
Steps to Solve
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Identify the Linear Equation Recognize that a linear equation typically has the form $Ax + By = C$.
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Rearrange to Slope-Intercept Form In order to convert the linear equation to slope-intercept form, you will rearrange it to the format $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept. This is done by solving for $y$.
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Solve for y If your original equation is $Ax + By = C$, subtract $Ax$ from both sides: $$ By = C - Ax $$
Then, divide each term by $B$ to isolate $y$: $$ y = -\frac{A}{B}x + \frac{C}{B} $$
This reveals both the slope $m$ and y-intercept $b$.
- Determine Values for x and y If specific values for either $x$ or $y$ are given, substitute them into the rearranged equation to solve for the other variable.
The slope-intercept form of the linear equation is $y = -\frac{A}{B}x + \frac{C}{B}$.
More Information
Converting a linear equation to slope-intercept form is crucial in understanding how the variables interact and in predicting values for $y$ based on $x$.
Tips
- Forgetting to isolate $y$ properly by not correctly simplifying each term or making algebraic errors.
- Confusing the slope and intercept after rearranging the terms.
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