Rewrite the following equation in slope-intercept form: y + 8 = –10(x − 6).
Understand the Problem
The question is asking to rewrite the equation in slope-intercept form ( y = mx + b ), where m is the slope and b is the y-intercept. The steps will involve distributing and isolating y.
Answer
$y = -\frac{2}{3}x + 2$
Answer for screen readers
The slope-intercept form is $y = -\frac{2}{3}x + 2$.
Steps to Solve
- Distribute the Equation
Start with the equation you have. If it's in the form of $Ax + By = C$, the first step is to isolate the $y$ variable. If there is a term that needs to be distributed, do so.
For example, from the equation $2x + 3y = 6$, we can distribute:
$$ 3y = 6 - 2x $$
- Isolate the y variable
Next, we need to isolate $y$ on one side of the equation. We can do this by dividing every term by the coefficient of $y$ or rearranging the equation.
Continuing the example above:
$$ y = \frac{6 - 2x}{3} $$
- Simplify the Equation
Now, simplify the equation if necessary.
From the previous step, we can separate the fraction:
$$ y = \frac{6}{3} - \frac{2}{3}x $$
This simplifies to:
$$ y = 2 - \frac{2}{3}x $$
- Rewrite in Slope-Intercept Form
Finally, rearranging the equation into the slope-intercept form:
$$ y = -\frac{2}{3}x + 2 $$
Here, $m = -\frac{2}{3}$ and $b = 2$.
The slope-intercept form is $y = -\frac{2}{3}x + 2$.
More Information
In the slope-intercept form equation $y = mx + b$, $m$ indicates how steep the line is (the slope), and $b$ indicates where the line crosses the y-axis (the y-intercept).
Tips
- Forgetting to distribute correctly can lead to errors; always check each term.
- When isolating $y$, some might mistakenly perform the wrong operation (like adding instead of subtracting). Always perform the same operation to both sides of the equation.
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