Put the following equation of a line into slope-intercept form, simplifying all fractions: x + y = 3.
Understand the Problem
The question is asking us to convert the equation of a line, given in standard form as x + y = 3, into slope-intercept form (y = mx + b), while simplifying any fractions that may arise during the process.
Answer
The slope-intercept form of the equation is \( y = -x + 3 \).
Answer for screen readers
The equation in slope-intercept form is:
$$ y = -x + 3 $$
Steps to Solve
- Rearranging the equation Start with the standard form equation:
$$ x + y = 3 $$
To isolate ( y ), subtract ( x ) from both sides:
$$ y = 3 - x $$
- Rearranging the equation into slope-intercept form Rewrite the equation to clearly show the slope-intercept form ( y = mx + b ):
$$ y = -x + 3 $$
- Identify the slope and intercept In the equation ( y = -x + 3 ):
- The slope ( m ) is ( -1 ).
- The y-intercept ( b ) is ( 3 ).
This confirms the slope-intercept form.
The equation in slope-intercept form is:
$$ y = -x + 3 $$
More Information
The slope-intercept form of a linear equation allows us to easily identify the slope and y-intercept. Here, the slope of ( -1 ) indicates that for every unit increase in ( x ), ( y ) decreases by 1. The y-intercept of 3 means the line crosses the y-axis at the point (0, 3).
Tips
- Not isolating ( y ): Ensure ( y ) is on one side by correctly subtracting ( x ) from both sides.
- Confusing coefficients: Make sure to correctly identify negative signs when rewriting the equation.
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