To find the slope of a line perpendicular to the given line $2x + 2y = 24$, let’s solve it step by step:

1. Rewrite the equation in slope-intercept form $y = mx + b$, where $m$ is the slope: $2x + 2y = 24$ Subtract $2x$ from both sides: $2y = -2x + 24$ Divide through by 2: $y = -x + 12$

   So, the slope of the given line is $m = -1$.

2. The slope of a line perpendicular to this one is the negative reciprocal of $-1$. The negative reciprocal is: $m_{\text{perpendicular}} = \frac{1}{1} = 1$

Final Answer:

The slope of the line perpendicular to the given line is 1.

Let me know if you need further explanation!

5 Related Questions:

1. How do you find the slope of a line given two points?
2. What is the formula for a line perpendicular to a given line through a specific point?
3. How can you determine if two lines are parallel or perpendicular from their equations?
4. What happens to the slope if a line is horizontal or vertical?
5. How do perpendicular slopes relate geometrically in a coordinate plane?

Tip:

To quickly find the slope of any line from its equation, always aim to rewrite it in the slope-intercept form $y = mx + b$.