Rewrite the following equation in slope-intercept form: y + 8 = -10(x - 6). 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 isolate y on one side of the equation to obtain the required form.
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 original equation
We start by identifying the equation that needs to be rewritten in slope-intercept form.
Assume the original equation is in standard form: $$ Ax + By = C $$
- Isolate the variable y
To rewrite the equation, we need to isolate y. We can do this by moving the term involving x to the other side:
$$ By = C - Ax $$
- Solve for y
Now, divide each term by B to solve for y:
$$ y = \frac{C}{B} - \frac{A}{B} x $$
- Rewrite in slope-intercept form
Now, we can rewrite this equation in the slope-intercept form $y = mx + b$:
Let $m = -\frac{A}{B}$ and $b = \frac{C}{B}$, thus the equation becomes:
$$ y = -\frac{A}{B} x + \frac{C}{B} $$
The equation in slope-intercept form is
$$ y = -\frac{A}{B} x + \frac{C}{B} $$
More Information
In the slope-intercept form, $m$ represents the slope of the line, which indicates the steepness and direction, while $b$ represents the y-intercept, the point where the line crosses the y-axis.
Tips
- Forgetting to correctly isolate y can lead to an incorrect slope-intercept form.
- Miscalculating the coefficients when dividing by B may result in an incorrect slope or y-intercept.
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