Respuesta :
Answer:
Therefore, equation of the line that passes through (-1,5) and is parallel to the line
[tex]2y+4x=-8[/tex]
is
[tex]y=-2x+3[/tex]
Step-by-step explanation:
Given:
[tex]2y+4x=-8[/tex] .Equation of line
can be written as
[tex]y=-2x-8[/tex] ...which is in Slope intercept form
To Find:
Equation of line passing through ( -1, 5) and is parallel to the line 2y+4x=-8
Solution:
[tex]y=-2x-8[/tex] ...........Given
Comparing with,
[tex]y=mx+c[/tex] ....general form in slope intercept
Where m =slope
We get
[tex]Slope = m = -2[/tex]
We know that parallel lines have Equal slopes.
Therefore the slope of the required line passing through (-1 , 5) will also have the slope = m = -2.
Now the equation of line in slope point form given by
[tex](y-y_{1})=m(x-x_{1})[/tex]
Substituting the points and so we will get the required equation of the line,
[tex](y-5)=-2(x-(-1))=-2(x+1)\\\\y-5=-2x-2\\y=-2x+3......Equation\ of\ line[/tex]
Therefore, equation of the line that passes through (-1,5) and is parallel to the line
[tex]2y+4x=-8[/tex]
is
[tex]y=-2x+3[/tex]
