Find the slope of a line parallel to the line whose equation is x + y = -4. Fully simplify your answer.
Understand the Problem
The question is asking for the slope of a line that is parallel to a given line represented by the equation x + y = -4. To solve this, we need to rearrange the equation into slope-intercept form and identify the slope.
Answer
The slope of a line parallel to the given line is \( -1 \).
Answer for screen readers
The slope of a line parallel to the given line is ( m = -1 ).
Steps to Solve
- Rearrange the equation to slope-intercept form
To find the slope of the line given by the equation ( x + y = -4 ), we need to rearrange it into the form ( y = mx + b ), where ( m ) is the slope.
Start by isolating ( y ): $$ y = -x - 4 $$
- Identify the slope
In the slope-intercept form ( y = mx + b ), ( m ) represents the slope. From the equation ( y = -x - 4 ), we can see that: $$ m = -1 $$
- Determine the slope of parallel lines
Lines that are parallel have the same slope. Therefore, the slope of any line parallel to the line represented by ( x + y = -4 ) is also: $$ m = -1 $$
The slope of a line parallel to the given line is ( m = -1 ).
More Information
This problem illustrates the concept that parallel lines share the same slope. The slope-intercept form ( y = mx + b ) is a useful way to quickly identify the slope of a linear equation.
Tips
- Confusing the intercepts and the slope: Remember, the slope is the coefficient of ( x ) in the slope-intercept form.
- Forgetting that parallel lines have the same slope: It's essential to remember that lines are parallel if they have identical slopes.
