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 smallest possible measurement of the width is 14 feet

step-by-step explanation:

let's assume length of parallelogram is 'l'

width of parallelogram is 'w'

the perimeter of a parallelogram must be no less than 40 feet

so, we get

we are given

length of parallelogram is 6 feet

so,

l=6

we can plug it

now, we can solve for w

subtract both sides by 12

divide both sides by 2

and we get

so,

the smallest possible measurement of the width is 14 feet

a

step-by-step explanation:

when a number is between two straight lines it means the absolute value.

to find absolute value you need to know how many numbers is that number away from 0.

when finding absolute value the number will always come out positive

so absolute value of -3 is 3

absolute value of 3/2 is 3/2

absolute value of -2 is 2

absolute value of 3.5 is 3.5

absolute value of -1 is 1

now put these numbers in order:

a)   |-1|, |3/2|, |-2|, |-3|, |3.5|