Answer:
[tex]y=\frac{1}{2}x+6[/tex]
Step-by-step explanation:
Given:
The equation of the known line is:
[tex]y=\frac{1}{2}x-4[/tex]
A point on the unknown line is (-4, 4)
Now, since the two lines are parallel, their slopes must be equal.
Now, slope of the known line is the coefficient of 'x' which is [tex]\frac{1}{2}[/tex].
Therefore, the slope of the unknown line is also [tex]m=\frac{1}{2}[/tex]
Now, for a line with slope 'm' and a point on it [tex](x_1,y_1)[/tex] is given as:
[tex]y-y_1=m(x-x_1)[/tex]
Here, [tex]m=\frac{1}{2}, x_1=-4,y_1=4[/tex]. Therefore,
[tex]y-4=\frac{1}{2}(x-(-4))\\\\y-4=\frac{1}{2}(x+4)\\\\y-4=\frac{1}{2}x+2\\\\y=\frac{1}{2}x+2+4\\\\y=\frac{1}{2}x+6[/tex]
Hence, the equation of the unknown line is [tex]y=\frac{1}{2}x+6[/tex].
