Mathematics, 02.06.2020 11:58 Fionaauggies

Write an equation of the line that passes through (2,−3) and is perpendicular to the line y=−2x−3.

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An equation of the line that passes through points (2,−3) and is perpendicular to the line is equal to $y=\frac{1}{2} x-4$

Given the following equation:

Points (x, y) = (2, -3)

First of all, we would determine the slope of the given equation:

Slope, m_1 = -2

In Mathematics, the slopes of two lines are said to be perpendicular when the product of these slopes is equal to negative one (-1).

Mathematically, this is given by;

$m_1 \times m_2 = -1$

Substituting the value of m_1 , we have:

$m_1 \times m_2 = -1\\\\-2 \times m_2 = -1\\\\m_2 = \frac{1}{2}$

The standard form of an equation of line is given by the formula;

y -y_1 =m(x-x_1)

Where:

x and y are the points.m is the slope.

Substituting the points into the formula, we have;

$y-y_1 =m(x-x_1)\\\\y-[-3] =\frac{1}{2} (x-2)\\\\y+3=\frac{1}{2} x -1\\\\y=\frac{1}{2} x-1 -3\\\\y=\frac{1}{2} x-4$

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Answer from: tykeria58

y = $\frac{1}{2}$ x - 4

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = - 2x - 3 ← is in slope- intercept form

with slope m = - 2

Given a line with slope m then the slope of a line perpendicular to it is

$m_{perpendicular}$ = - $\frac{1}{m}$ = - $\frac{1}{-2}$ = $\frac{1}{2}$ , thus

y = $\frac{1}{2}$ x + c ← is the partial equation

To find c substitute (2, - 3) into the partial equation

- 3 = 1 + c ⇒ c = - 3 - 1 = - 4

y = $\frac{1}{2}$ x - 4 ← equation of perpendicular line

Answer from: Quest

$w\geq 14$

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

$2l+2w\geq 40$

we are given

length of parallelogram is 6 feet

so,

l=6

we can plug it

$2\times 6+2w\geq 40$

now, we can solve for w

$12+2w\geq 40$

subtract both sides by 12

$12+2w-12\geq 40-12$

$2w\geq 28$

divide both sides by 2

and we get

$w\geq 14$

so,

the smallest possible measurement of the width is 14 feet

Answer from: Quest

see explanation

step-by-step explanation:

(6r + 7) + (13 + 7r) ( remove brackets and collect like terms )

= 6r + 7 + 13 + 7r

= 13r + 20

remove brackets and collect like terms

13 - $\frac{3}{2}$ r - 1 + r

= 12 - $\frac{1}{2}$ r

remove brackets and collect like terms

= - 8 - r + 2r - 4

= - 12 + r

remove brackets and collect like terms

= 7r - $\frac{3}{2}$ - $\frac{2}{3}$ - 6r

[- $\frac{3}{2}$ - $\frac{2}{3}$ = - $\frac{9}{6}$ - $\frac{4}{6}$ = - $\frac{13}{6}$ ]

= r - $\frac{13}{6}$

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Write an equation of the line that passes through (2,−3) and is perpendicular to the line y=−2x−3....