Find the slope-intercept form of an equation of the line perpendicular to the graph of x - 3y = 5 and passes through (0,6).
a. y = 1/3x + 2
b. y = 3x - 6
c. y = 1/3x - 2
d. 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

Substitute M = -3 and the point (0,6) in the point-slope form of the equation as shown

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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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 correct answer is x/3+10≥32

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