Find the slope of a line perpendicular to the line whose equation is 3, x, minus, 5, y, equals, 453x−5y=45. Fully simplify your answer.
Question
Find the slope of a line perpendicular to the line whose equation is 3, x, minus, 5, y, equals, 453x−5y=45. Fully simplify your answer.
Solution
The equation of the line given is 3x - 5y = 45.
Step 1: Convert this equation into slope-intercept form (y = mx + b), where m is the slope of the line.
To do this, we isolate y:
3x - 5y = 45 -5y = -3x + 45 y = 3/5x - 9
So, the slope (m) of the given line is 3/5.
Step 2: The slope of a line perpendicular to a given line is the negative reciprocal of the slope of the given line.
The reciprocal of 3/5 is 5/3.
Therefore, the slope of the line perpendicular to the given line is -5/3.
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