Rewrite the following equation in slope-intercept form: –7x + 8y = –19. Write your answer using integers, proper fractions, and improper fractions in simplest form.
Understand the Problem
The question is asking to convert the given linear equation from its standard form to slope-intercept form, which follows the format y = mx + b where m is the slope and b is the y-intercept.
Answer
The slope-intercept form is $y = -\frac{A}{B}x + \frac{C}{B}$.
Answer for screen readers
Given the linear equation in standard form $Ax + By = C$, the slope-intercept form is:
$$ y = -\frac{A}{B}x + \frac{C}{B} $$
Steps to Solve
- Identify the standard form of the equation
Start with the given standard form of the linear equation, which is typically represented as $Ax + By = C$.
- Isolate the y variable
Rearrange the equation to solve for $y$. Subtract $Ax$ from both sides to isolate $By$ on the left side:
$$ By = -Ax + C $$
- Divide by the coefficient of y
To get $y$ by itself, divide all terms in the equation by the coefficient of $y$ (which is $B$):
$$ y = -\frac{A}{B}x + \frac{C}{B} $$
- Identify slope and y-intercept
Now, the equation is in the slope-intercept form $y = mx + b$. The slope $m$ is $-\frac{A}{B}$, and the y-intercept $b$ is $\frac{C}{B}$.
Given the linear equation in standard form $Ax + By = C$, the slope-intercept form is:
$$ y = -\frac{A}{B}x + \frac{C}{B} $$
More Information
Converting from standard form to slope-intercept form makes it easier to find the slope and y-intercept of the line. This form is particularly useful in graphing and understanding the relationship between the variables.
Tips
Common mistakes include:
- Forgetting to distribute the negative sign when isolating $y$.
- Not dividing each term by the coefficient of $y$, leading to incorrect slope and intercept values.
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