Answer:
the desired equation is y = -3x + 6.
Step-by-step explanation:
1) Rewrite x - 3y = 5 in slope-intercept form: x - 5 = 3y, or y = (1/3)(x - 5)
2) Identify the slope of the given line. It is (1/3).
3) Find the slope of a line perpendicular to this one. It is the negative reciprocal of (1/3), or -3.
4) Use the slope-intercept form of the equation of a straight line, y = mx + b, to determine the b value and thus the equation of the perpendicular line:
6 = -3(0) + b. Then b = 6, and the desired equation is y = -3x + 6.
The slope-intercept form of an equation of the line perpendicular to the graph of x - 3y = 5 and passes through (0,6) is y = -3x + 6
The slope is the ratio of the rise of a line to its run. The slope of a line determines its steepness.
The general formula for finding the equation of a straight line in point-slope form is expressed as:
y- y₀= m(x-x₀) where:
m is the slope
(x₀, y₀) is a point on the line.
Get the slope from the equation x - 3y = 5
Write in standard form y = m+b
3y = x - 5
y = x/3 - 5/3
This shows that m = 1/3
Since the equation of the line needed is perpendicular to the graph of x - 3y = 5, hence:
Required slope
[tex]M = \frac{-1}{m}\\ M=\frac{-1}{\frac{1}{3} } \\M=-3[/tex]
Substitute M = -3 and the point (0,6) in the point-slope form of the equation as shown
[tex]y-6=-3(x-0)\\y-6=-3x\\y=-3x+6[/tex]
Hence the slope-intercept form of an equation of the line perpendicular to the graph of x - 3y = 5 and passes through (0,6) is y = -3x + 6
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