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3 years ago

What is the equation of the line that passes through the point (5, -2) and has a slope of 6/5

Mathematics

1 answer:

liubo4ka [24]3 years ago

5 0

Answer:

y + 2 = ⁶/₅(x - 5) {the point-slope form of the equation}

y = ⁶/₅x - 8 {the slope-intercept form of the equation}

6x - 5y = 40 {the standard form of the equation}

Step-by-step explanation:

The point-slope form of equation is: y - y₀ = m(x - x₀), where (x₀, y₀) is any point the line passes through and m is the slope.

m = ⁶/₅

(5, -2) ⇒ x₀ = 5, y₀ = -2

So, the point-slope form of the equation:

y + 2 = ⁶/₅(x - 5)

Therefore:

y + 2 = ⁶/₅x - 6 {subtract 2 from both sides}

y = ⁶/₅x - 8 ← the slope-intercept form of the equation

-⁶/₅x + y = - 8 {multiply both sides by (-5)}

6x - 5y = 40 ← the standard form of the equation

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3 years ago

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Ipatiy [6.2K]

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3 years ago

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grandymaker [24]

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3 years ago

Read 2 more answers

Use linear approximation to estimate f (2.85 )given that f (3 )equals 2 and f prime (3 )equals 5.

Allisa [31]

Answer:

Step-by-step explanation:

Given that,

f(3) = 2

f'(3) = 5.

We want to estimate f(2.85)

The linear approximation of "f" at "a" is one way of writing the equation of the tangent line at "a".

At x = a, y = f(a) and the slope of the tangent line is f'(a).

So, in point slope form, the tangent line has equation

y − f(a) = f'(a)(x − a)

The linearization solves for y by adding f(a) to both sides

f(x) = f(a) + f'(a)(x − a).

Given that,

f(3) = 2,

f'(3) = 5

a = 3, we want to find f(2.85)

x = 2.85

Therefore,

f(x) = f(a) + f'(a)(x − a)

f(2.85) = 2 + 5(2.85 - 3)

f(2.85) = 2 + 5×-0.15

f(2.85) = 2 - 0.75

f(2.85) = 1.25

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3 years ago