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julia-pushkina [17]
3 years ago
6

Consider the line y = 3x - 1.

Mathematics
1 answer:
padilas [110]3 years ago
8 0

Answer:

y = -1/3x + 1/3

Step-by-step explanation:

The slopes of perpendicular lines are negative reciprocals.

The given line is

y = 3x - 1

This equation is written in the slope-intercept form, y = mx + b, where m is the slope.

slope of given line = m = 3

slope of perpendicular line = -1/3

Now we need the equation of the line with slope -1/3 that passes through the point (-8, 3)

y = mx + b

y = -1/3x + b

3 = (-1/3)(-8) + b

3 = 8/3 + b

9/3 = 8/3 + b

b = 1/3

y = -1/3x + b

y = -1/3x + 1/3

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Question in the photo
yaroslaw [1]

Using translation concepts, the equation of g(x) is given as follows:

g(x) = -\frac{35}{x + 10} - 1

<h3>What is a translation?</h3>

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s definition or in it’s domain. Examples are shift left/right or bottom/up, vertical or horizontal stretching or compression, and reflections over the x-axis or the y-axis.

For this problem, the parent function is given by:

f(x) = \frac{1}{x}

For a horizontal compression by a factor of 1/5, we have to find f(1/5x), hence:

g(x) = \frac{1}{\frac{1}{5}}x = \frac{5}{x}

For a vertical stretch by a factor of 7, we have to multiply by 7, hence:

g(x) = \frac{35}{x}

For a reflection in the y-axis, we have to find g(-x), hence:

g(x) = \frac{35}{-x} = -\frac{35}{x}

For a translation of 10 units left, we have to find g(x + 10), hence:

g(x) = -\frac{35}{x + 10}

For a translation of 1 unit down, we have to subtract one, hence:

g(x) = -\frac{35}{x + 10} - 1

More can be learned about translation concepts at brainly.com/question/28174785

#SPJ1

8 0
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Step-by-step explanation:

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