Equation of the line passes through point (4,-7) and parallel to[tex]y= \frac{-2}{3}x+\frac{3}{2}[/tex]is equals to [tex]y = \frac{-2}{3}x-\frac{13}{3}[/tex].
What is parallel lines?
" Parallel lines are defined as the different sets of lines in the same plane are equidistant to each other and never intersect in the same plane. Slope of the parallel lines are always equal. "
Formula used
Equation of the line,
[tex]y-y_{1} = m (x-x_{1})[/tex]
'm' = slope of the line
line passes through points = [tex]( x_{1}, y_{1})[/tex]
According to the question,
Given equation of line,
[tex]y= \frac{-2}{3}x+\frac{3}{2}[/tex]
Slope [tex]m_{1} =\frac{-2}{3}[/tex]
[tex]'m_{2}'[/tex] represent the slope of the required line parallel to the given line
Slope of the parallel lines are equal ,
Therefore,
[tex]m_{1} = m_{2}\\\\\implies m_{2} = \frac{-2}{3}[/tex]
Line passes through the points [tex]( x_{1}, y_{1}) = (4,-7)[/tex]
Substitute the value in the formula to get the equation of line parallel to the given line,
[tex]y-(-7) = \frac{-2}{3}(x-4)\\ \\\implies y +7 = \frac{-2}{3}x + \frac{8}{3} \\\\\implies y = \frac{-2}{3}x + \frac{8}{3} -7\\\\\implies y = \frac{-2}{3}x - \frac{13}{3}[/tex]
Hence, equation of the line passes through point (4,-7) and parallel to[tex]y= \frac{-2}{3}x+\frac{3}{2}[/tex]is equals to [tex]y = \frac{-2}{3}x-\frac{13}{3}[/tex].
Learn more about parallel lines here
https://brainly.com/question/16701300
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