Given:
The given equation of the line is [tex]y=\frac{1}{4}x+2[/tex]
The line that is parallel to the given line passes through the point (12,-25)
We need to determine the equation of the line.
Slope:
Since, the two lines are parallel, then their slope must be same.
Thus, from the equation [tex]y=\frac{1}{4}x+2[/tex], the slope is given by
[tex]m=\frac{1}{4}[/tex]
Thus, the slope of the parallel line is [tex]m=\frac{1}{4}[/tex]
Equation of the line:
The equation of the line can be determined using the formula,
[tex]y-y_1=m(x-x_1)[/tex]
Substituting the slope and the point (12,-25), we have;
[tex]y+25=\frac{1}{4}(x-12)[/tex]
[tex]y+25=\frac{1}{4}x-3[/tex]
[tex]y=\frac{1}{4}x-28[/tex]
Thus, the equation of the line is [tex]y=\frac{1}{4}x-28[/tex]
