Line y = -2x - 1 is transformed by dilation with a scale factor of 2 and centered at (1,-3). Write the equation of lines image

The y value is equivalent to the centre of dilation, the equation of the line image will be equal to y = -2x - 1

The standard form of an equation is expressed as y = mx + b

m is the slope of the line

b is the y-intercept

Given the equation of a line expressed as y = -2x - 1

If the line is transformed by dilation with a scale factor of 2 and centred at (1, -3)

First, we will need to find the y-value for which x = 1

y = -2(1) - 1

y = -2 - 1

y = -3

Since the y value is equivalent to the centre of dilation, the equation of the line image will be equal to y = -2x - 1

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Step-by-step explanation:

The given equation of line is

The above line dilated with a scale factor of 2 and centered at (1,-3).

Substitute in the given equation.

The line passing through (1,-3). It means, the given line passing through the center of dilation.

We know that if a line passes through the center of the dilation, then nothing will change and equation of image is same as the equation of line.

So, the equation of image of line is .

The number of revolutions per minute that are made by the tire is 110

Step-by-step explanation:

step 1

Find the circumference of the tire

The circumference of a circle is

we have

1 ft=12 in

Convert in to ft

----> the radius is half the diameter

substitute

Remember that one revolution represent the length of the circumference

so

using proportion

Find out how many revolutions are made by the tire in one minute

Let

x -----> the number of revolutions in one minute

therefore

The number of revolutions per minute that are made by the tire is 110