What is the slope of a line parallel to [tex]$y=\frac{5}{2} x-7$[/tex]?
Answer (1)
Identify the slope of the given line y = 2 5 x − 7 by comparing it to the slope-intercept form y = m x + b .
Recall that parallel lines have the same slope.
The slope of the given line is 2 5 .
Therefore, the slope of a line parallel to the given line is 2 5 .
Explanation
Understanding the Problem We are given the equation of a line: y = 2 5 x − 7 . We need to find the slope of a line that is parallel to this line.
Key Concept: Parallel Lines Recall that parallel lines have the same slope. The equation of a line in slope-intercept form is y = m x + b , where m represents the slope and b represents the y-intercept.
Identifying the Slope Comparing the given equation y = 2 5 x − 7 with the slope-intercept form y = m x + b , we can identify the slope of the given line as m = 2 5 .
Finding the Parallel Slope Since parallel lines have the same slope, the slope of a line parallel to the given line is also 2 5 .
Final Answer Therefore, the slope of a line parallel to y = 2 5 x − 7 is 2 5 .
Examples
Imagine you're drawing lines on a graph. If you want to draw a line that runs alongside the line y = 2 5 x − 7 without ever intersecting it, you need to make sure it has the same steepness. In mathematical terms, this steepness is the slope. So, any line parallel to y = 2 5 x − 7 will also have a slope of 2 5 . This concept is useful in architecture, where parallel lines are frequently used in building design, ensuring walls and beams are aligned correctly.
