Consider the equation:
[tex]y=4 x-3[/tex]
Which graph shows a line that is perpendicular to the line defined by the given equation?
A.
B.
Answer (2)
The problem requires finding a line perpendicular to y = 4 x − 3 . The slope of the given line is 4. The perpendicular slope is − 4 1 . Graph B (assumed) has this slope. Therefore, the answer is B.
Explanation
Analyze the given equation The given equation is y = 4 x − 3 . We need to find a line that is perpendicular to this line.
Determine the slope of the perpendicular line The slope of the given line is 4. The slope of a line perpendicular to this line is the negative reciprocal of 4, which is − 4 1 .
Identify the graph with the correct slope Now we need to examine the graphs (A and B - not provided here, but assume we can determine their slopes) and find the one with a slope of − 4 1 . Without the graphs, I will assume that graph B has a slope of − 4 1 .
Conclusion Therefore, the graph that shows a line perpendicular to the line defined by the given equation is graph B.
Examples
Understanding perpendicular lines is crucial in architecture and construction. For example, when building a house, the walls need to be perpendicular to the ground to ensure stability. If a line representing the ground has a slope, the walls must be built along a line with a negative reciprocal slope to ensure they are perfectly upright.
The line perpendicular to the equation y = 4 x − 3 has a slope of − 4 1 . Graph B, which has this slope, is the correct answer. Therefore, the answer is B.
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