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3 years ago

Find the equation of a line that runs through

Mathematics

1 answer:

MAVERICK [17]3 years ago

7 0

Answer:

The equation of a line that runs through (-6,2) and is parallel to a line with a slope of (-1/4) is x + 4y - 2 = 0

Step-by-step explanation:

Slope of the parallel equation is m 1 = (-1/4)

If the two liner are parallel the, slope of both lines are equal.

⇒The slope of the equation of line = m2 = m1 = -(1/4)

The point (x0, y0) = (-6,2)

Now, by THE POINT SLOPE FORMULA: The equation of a line is given as

( y - y0) = m (x -x0)

Now, here the equation of line is given as:

$y - 2 = (\frac{-1}{4}) (x - (-6)) \implies 4(y-2) = -1(x + 6)$

or, 4y - 8 + x + 6 = 0

or, x + 4y - 2 = 0

Hence, the required line equation is x + 4y - 2 = 0

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3 years ago

Suppose a certain home improvement outlet knows that the monthly demand for framing studs is 2,300 when the price is $4.77 each

pogonyaev

Answer:

p + 0.0001q = 5

Step-by-step explanation:

Data provided in the question:

When Price, p₁ = $4.77 ; Demand, q₁ = 2,300

and,

When Price, p₂ = 3,300 ; Demand, q₂ = 3,300

considering the above as the points on the line,

now, the general equation for a line is given as:

$\frac{q_1-q}{p_1-p}=\frac{q_2-q_1}{p_2-p_1}$

on substituting the respective values, we get

$\frac{2,300-q}{4.77-p}=\frac{3,300-2,300}{4.67-4.77}$

$\frac{2,300-q}{4.77-p}=\frac{1000}{-0.1}$

2,300 - q = -10,000(4.77 - p)

⇒ 2,300 - q = -47700 + 10,000p

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⇒ 10,000p + q = 50000

⇒ p + 0.0001q = 5

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3 years ago