Given x + 3y = -6, identify the slope and y-intercept.
Understand the Problem
The question is asking us to identify the slope (m) and y-intercept (b) of the linear equation given in the form x + 3y = -6. To solve it, we will rearrange the equation into the slope-intercept form (y = mx + b).
Answer
Slope \( m = -\frac{1}{3} \), Y-intercept \( b = -2 \)
Answer for screen readers
Slope ( m = -\frac{1}{3} )
Y-intercept ( b = -2 )
Steps to Solve
- Rearranging the equation
We start with the equation ( x + 3y = -6 ). To put it in slope-intercept form ( y = mx + b ), we need to isolate ( y ).
- Isolate ( 3y )
Subtract ( x ) from both sides: $$ 3y = -x - 6 $$
- Divide by 3
Now, divide every term by 3 to isolate ( y ): $$ y = -\frac{1}{3}x - 2 $$
- Identify the slope and y-intercept
From the equation ( y = mx + b ), we can identify the slope ( m ) and the y-intercept ( b ):
- The slope ( m = -\frac{1}{3} )
- The y-intercept ( b = -2 )
Slope ( m = -\frac{1}{3} )
Y-intercept ( b = -2 )
More Information
In slope-intercept form ( y = mx + b ), ( m ) represents the slope of the line, which indicates the steepness and direction, while ( b ) represents the point where the line crosses the y-axis. Here, the line slopes downwards as ( m ) is negative.
Tips
- Forgetting to properly isolate ( y ) can lead to an incorrect slope or y-intercept.
- Confusion about the signs during rearrangement can also lead to errors in identifying ( m ) and ( b ).