Given:
The equation of the parallel line is
[tex]y=-\dfrac{5}{2}x+7[/tex]
The required line passes through the point (-4,1).
To find:
The equation of line in slope slope intercept form.
Solution:
The slope intercept form of a linear function is
[tex]y=mx+b[/tex]
Where m is slope and b is y-intercept.
On comparing the equation [tex]y=-\dfrac{5}{2}x+7[/tex] with slope intercept form, we get
[tex]m=-\dfrac{5}{2}[/tex]
We know that the slopes of parallel lines are always same. So, the slope of the required line is [tex]m=-\dfrac{5}{2}[/tex].
The line passes through the point (-4,1) with slope [tex]m=-\dfrac{5}{2}[/tex]. So, the equation of line is
[tex]y-y_1=m(x-x_1)[/tex]
[tex]y-(1)=-\dfrac{5}{2}(x-(-4))[/tex]
[tex]y-1=-\dfrac{5}{2}(x+4)[/tex]
[tex]y-1=-\dfrac{5}{2}x-10[/tex]
Adding 1 on both sides, we get
[tex]y=-\dfrac{5}{2}x-10+1[/tex]
[tex]y=-\dfrac{5}{2}x-9[/tex]
Therefore, the correct option is C.