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3 years ago

Write the equation of line in slope-intercept form. Line parallel to y=−2x+3 that passes through the point (−100,−100)

Mathematics

2 answers:

Tems11 [23]3 years ago

4 0

The line with equation y = -2x + 3 has a slope of -2

The line parallel to line with equation y = -2x + 3 has a slope of -2

This is because parallel lines have the same slope

Taking a point (x,y) along the parallel line passing through (-100,-100)

Slope = change in y-axis divide by change in x-axis

-2 = (y - -100) ÷ (x - -100)

-2(x + 100) = y + 100

y = -2x - 300

GrogVix [38]3 years ago

3 0

Remark

The line you want is parallel to y = - 2x + 3

That means it has the same slope as the given line. The given line has a slope of -2

y = -2x + b is what you have so far. Now you have to use the point to get b

y = - 100

x = - 100

Solve for b

-100 = -2(-100) + b

-100 = 200 + b Notice the sign change. Two minus's make a plus. Subtract 200 from both sides.

- 100 - 200 = b

- 300 = b

Answer

y = - 2x - 100

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$\frac{1}{x} +\frac{1}{y} = 5\\\\x^{-1}+y^{-1}=5\\$

Above, I changed the fraction form of x and y into exponential form so it is easier to see the differentiation. Now, we can differentiate:

$-1x^{-2}+-1y^{-2}\frac{dy}{dx}=5\\\\\frac{-1}{x^2}-\frac{1}{y^2}\frac{dy}{dx}=5\\\\-\frac{1}{y^2}\frac{dy}{dx}=5+\frac{1}{x^2}\\\\\frac{dy}{dx}=-5y^2-\frac{y^2}{x^2}$

Now that we have dy/dx, we can plug in the x, which is 4, and the y, which is 4/19. We know these values of x and y because your question stated y(4) = 4/19.

$\frac{dy}{dx}=-5(\frac{4}{19})^2-\frac{(\frac{4}{19})^2}{(4)^2}\\\\\frac{dy}{dx}=-5(\frac{16}{361})-\frac{(\frac{16}{361})}{16}\\\\\frac{dy}{dx}=\frac{-80}{361}-\frac{1}{361}\\\\\frac{dy}{dx}=\frac{-81}{361}$

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