What is the slope of a line that is parallel to [tex]$y=-\frac{1}{2} x-10$[/tex]?
A. -2
B. -[tex]$\frac{1}{2}$[/tex]
C. [tex]$\frac{1}{2}$[/tex]
D. 2
Answer (1)
Identify the slope of the given line y = − 2 1 x − 10 as − 2 1 .
Recall that parallel lines have the same slope.
Conclude that the slope of a line parallel to the given line is also − 2 1 .
The slope of the parallel line is − 2 1 .
Explanation
Understanding the Problem We are given the equation of a line: y = − 2 1 x − 10 . We need to find the slope of a line that is parallel to this line.
Identifying the Slope The given equation is in slope-intercept form, which is y = m x + b , where m is the slope and b is the y-intercept. In our case, m = − 2 1 and b = − 10 . So, the slope of the given line is − 2 1 .
Finding the Parallel Slope Parallel lines have the same slope. Therefore, the slope of any line parallel to the given line y = − 2 1 x − 10 is also − 2 1 .
Final Answer The slope of a line parallel to y = − 2 1 x − 10 is − 2 1 .
Examples
Imagine you're drawing lines on a graph. If you want to draw a line that runs alongside the line y = − 2 1 x − 10 without ever crossing it, you need to make sure it has the same 'steepness' or slope. In this case, the slope is − 2 1 , which means for every 2 units you move to the right, you move 1 unit down. This concept is useful in architecture, where parallel lines are essential for designing buildings and structures, ensuring walls and beams are aligned correctly.
