Find the slope of a line parallel to the line whose equation is x + y = -4. Fully simplify your answer.

Question image

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

  1. 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 ): $$ y = -x - 4 $$

  1. 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: $$ m = -1 $$

  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.
Thank you for voting!
Use Quizgecko on...
Browser
Browser