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2 years ago

Through: (1, 3), perp. to y = x + 5

Mathematics

1 answer:

MAXImum [283]2 years ago

8 0

Answer:

y = 3x + 2

Step-by-step explanation:

Convert the equation to slope intercept form to get y = –1/3x + 2. The old slope is –1/3 and the new slope is 3. Perpendicular slopes must be opposite reciprocals of each other: m1 * m2 = –1

With the new slope, use the slope intercept form and the point to calculate the intercept: y = mx + b or 5 = 3(1) + b, so b = 2

So y = 3x + 2

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Answer:

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Step-by-step explanation:

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3 years ago

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3 years ago

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3 years ago

Read 2 more answers

The slope of a line is 0 and it contains the point (3,1)

Sedaia [141]

Answer:

Step-by-step explanation:

The point-slope form of an equation of a line:

$y-y_1=m(x-x_1)$

m - slope

(x₁, y₁) - point on a line

We have m = 0, (3, 1) → x₁ = 3, y₁ = 1.

Substitute:

$y-1=0(x-3)$

$y-1=0$ add 1 to both sides

$y=1$

Other method.

If the slope is equal 0, then it's a horizontal line.

The equation of a horizontal line: y = a.

We have the point on a line (3, 1) → x = 3, y = 1.

Therefore the equation is y = 1.

3 0

3 years ago

Consider parent function f(x)=e^x and the transformes function g(x)= -1/2e^3x+4, quantitatively explain the transformations to t

kolezko [41]

Answer: reflection across the x-axis

vertical shrink by a factor of 1/2

horizontal shrink by a factor of 1/3

vertical shift up 4 units

Step-by-step explanation:

$\text{Note:}\ g(x) = -Ae^{Bx-C}+D\\\bullet \quad \text{- represents a reflection across the x-axis}\\\\\bullet \quad \text{A represent a vertical stretch by a factor of A (shrink if}\ |A| < 1)\\\\\bullet \quad \text{B represents a horizontal stretch by a factor of}\ \dfrac{1}{B}\ (\text{shrink if}\ |B| >1) \\\\\bullet \quad \text{C represents a horizontal shift of C units}\ (\text{+ is right, - is left}) \\\\\bullet \quad \text{D represents a vertical shift of D units}\ (\text{+ is up, - is down})$

$\text{Parent function:}\ f(x)=e^x\\\text{Transformed function:}\ g(x)=-\dfrac{1}{2}e^{3x}+4\\$

The transformed function has the following:

Negative: reflection across the x-axis

A = 1/2 vertical shrink by a factor of 1/2

B = 3 horizontal shrink by a factor of 1/3

C = 0 no horizontal shift

D = 4 vertical shift of 4 units up

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3 years ago