Find the slope of a line perpendicular to the line whose equation is 3, x, minus, 6, y, equals, 903x−6y=90. Fully simplify your answer.
Question
Find the slope of a line perpendicular to the line whose equation is 3, x, minus, 6, y, equals, 903x−6y=90. Fully simplify your answer.
Solution
The equation of the line given is 3x - 6y = 90.
Step 1: Convert this equation into slope-intercept form (y = mx + b), where m is the slope of the line.
To do this, we first isolate y.
3x - 6y = 90 -6y = -3x + 90 y = 1/2x - 15
Step 2: Identify the slope of the given line.
From the equation y = 1/2x - 15, we can see that the slope (m) of the line is 1/2.
Step 3: Find the slope of the line that is perpendicular to the given line.
The slope of a line perpendicular to a given line is the negative reciprocal of the slope of the given line.
The negative reciprocal of 1/2 is -2.
Therefore, the slope of the line perpendicular to the given line is -2.
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