Answer:
[tex]y=-2x-1[/tex] .
Step-by-step explanation:
The given equation of line is
[tex]y=-2x-1[/tex]
The above line dilated with a scale factor of 2 and centered at (1,-3).
Substitute [tex]x=1[/tex] in the given equation.
[tex]y=-2(1)-1[/tex]
[tex]y=-2-1[/tex]
[tex]y=-3[/tex]
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 [tex]y=-2x-1[/tex].
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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