Given x + 3y = -6, identify the slope and y-intercept.
Understand the Problem
The question is asking to identify the slope (m) and y-intercept (b) of the equation given in the format x + 3y = -6. This requires rearranging the equation into the slope-intercept form (y = mx + b).
Answer
m = $-\frac{1}{3}$, b = $-2$
Answer for screen readers
m = $-\frac{1}{3}$
b = $-2$
Steps to Solve
- Rearranging the equation
Start with the original equation: $$ x + 3y = -6 $$
Subtract $x$ from both sides to isolate the term with $y$: $$ 3y = -x - 6 $$
- Dividing to solve for y
Next, divide every term by 3 to solve for $y$: $$ y = -\frac{1}{3}x - 2 $$
- Identifying the slope and y-intercept
From the slope-intercept form of the equation $y = mx + b$, we can directly read off the values:
- The slope $m = -\frac{1}{3}$
- The y-intercept ( b = -2 )
m = $-\frac{1}{3}$
b = $-2$
More Information
The slope ($m$) indicates that for each increase of 1 unit in $x$, $y$ decreases by $\frac{1}{3}$ units. The y-intercept ($b$) shows that when $x = 0$, $y$ will be $-2$.
Tips
- Forgetting to divide every term by the same number when rearranging.
- Confusing the slope and y-intercept after obtaining the equation.
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