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2 years ago

Write an equation in point-slope form for the line that has a slope of 4/5 and contains the point (−5, −3).

Mathematics

1 answer:

ankoles [38]2 years ago

5 0

y = mx + b, where m = slope, and b = y-intercept.

Since you are not given the y-intercept, you have to solve for it through the equation, y = (4/5)x (which is the slope you are given) + b, and replace x and y with values given, which are (-5,-3)

y = (4/5)x + b

-3 = (4/5)(-5) + b

-3 = -4 + b

1 = b

Then replace b in the first equation to get the answer

y = (4/5)x + 1

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Which equation describes a line parallel to y= 4x+ 5 through point (-2, 1)?

Keith_Richards [23]

The line parallel to y= 4x+ 5 passing through point (-2, 1) is y = 4x + 9

<h3>Parallel Equations</h3>

The given equation is:

y = 4x + 5

Compare y = 4x + 5 with the equation y = mx + c

m = 4, c = 5

The equation parallel to y = 4x + 5 will also have a slope, m = 4

The point-slope form of the equation of a line is given as:

y - y₁ = m(x - x₁)

substitute m = 4, x₁ = -2 and y = 1 into the equation above

y - 1 = 4(x - (-2)

y - 1 = 4(x + 2)

y - 1 = 4x + 8

y = 4x + 8 + 1

y = 4x + 9

Therefore the line parallel to y= 4x+ 5 passing through point (-2, 1) is y = 4x + 9

Learn more on equation of a line here: brainly.com/question/13763238

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2 years ago

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2 years ago

1 pt) If a parametric surface given by r1(u,v)=f(u,v)i+g(u,v)j+h(u,v)k and −4≤u≤4,−4≤v≤4, has surface area equal to 1, what is t

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The area of the surface given by $\vec r_1(u,v)$ is 1. In terms of a surface integral, we have

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By multiplying each component in $\vec r_1$ by 5, we have

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and the same goes for the derivative with respect to $v$ . Then the area of the surface given by $\vec r_2(u,v)$ is

$\displaystyle\int_{-4}^4\int_{-4}^425\left\|\frac{\partial\vec r_1(u,v)}{\partial u}\times\frac{\partial\vec r_1(u,v)}{\partial v}\right\|\,\mathrm du\,\mathrm dv=\boxed{25}$

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Answer:

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Step-by-step explanation:

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The area of a rhombus is 90 square inches. If the longer diagonal measures 18 inches, what is the length of the shorter diagonal

lorasvet [3.4K]

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