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 us to rewrite the given equation in slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept. We will need to isolate y on one side of the equation.
Answer
$$ y = -\frac{A}{B}x + \frac{C}{B} $$
Answer for screen readers
The equation in slope-intercept form is:
$$ y = -\frac{A}{B}x + \frac{C}{B} $$
Steps to Solve
- Identify the equation to rewrite Start with the given equation, which we need to convert into slope-intercept form. Assume the equation is given as:
$$ Ax + By = C $$
- Isolate the term with y To isolate $y$, we need to move $Ax$ to the other side of the equation. This involves subtracting $Ax$ from both sides.
$$ By = C - Ax $$
- Solve for y Next, we divide every term by $B$ to get $y$ by itself.
$$ y = \frac{C}{B} - \frac{A}{B}x $$
- Rewrite in the slope-intercept form Finally, we can rewrite this in the form $y = mx + b$, identifying the slope ($m$) and the y-intercept ($b$).
Here, $\frac{-A}{B}$ is the slope and $\frac{C}{B}$ is the y-intercept. So, we write it as:
$$ y = -\frac{A}{B}x + \frac{C}{B} $$
The equation in slope-intercept form is:
$$ y = -\frac{A}{B}x + \frac{C}{B} $$
More Information
In this form, you can easily identify the slope and y-intercept of the line represented by the equation. The slope tells you how steep the line is, while the y-intercept indicates where the line crosses the y-axis.
Tips
- Forgetting to move all terms involving $y$ to one side of the equation.
- Ignoring to divide by the coefficient of $y$ when isolating it.
- Mixing up the signs when rearranging the equation.
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