Which line is parallel to the line [tex]$8 x+2 y=12$[/tex]?
Answer (2)
Rewrite the given equation 8 x + 2 y = 12 in slope-intercept form.
Determine the slope of the line, which is − 4 .
Identify that any line parallel to the given line must also have a slope of − 4 .
Conclude that a line parallel to 8 x + 2 y = 12 has a slope of − 4 .
Explanation
Understanding the Problem We are given the equation of a line: 8 x + 2 y = 12 . Our goal is to find another line that is parallel to this one. Parallel lines have the same slope. Therefore, we need to determine the slope of the given line.
Finding the Slope To find the slope, we can rewrite the equation in slope-intercept form, which is y = m x + b , where m is the slope and b is the y-intercept. Let's rearrange the given equation to this form:
8 x + 2 y = 12
Subtract 8 x from both sides:
2 y = − 8 x + 12
Divide both sides by 2:
y = − 4 x + 6
Now we can see that the slope of the given line is − 4 .
Identifying Parallel Lines Any line parallel to the given line will also have a slope of − 4 . Therefore, we are looking for a line with the same slope. For example, the line y = − 4 x + 5 is parallel to the given line.
Examples
Understanding parallel lines is crucial in architecture and construction. When designing buildings, architects use parallel lines to create stable and visually appealing structures. For example, walls, floors, and ceilings are often designed to be parallel to each other to ensure structural integrity and aesthetic harmony. The concept of slope is also vital in designing ramps and determining the steepness of roofs, ensuring they meet safety and functionality standards. By applying these mathematical principles, architects can create safe, efficient, and visually pleasing buildings.
To find a parallel line to 8 x + 2 y = 12 , we first convert it to slope-intercept form, yielding a slope of − 4 . Any line with a slope of − 4 , such as y = − 4 x + 3 , will be parallel. In general, lines of the form y = − 4 x + b are parallel to the original line.
;
