Given the equation of the line :
[tex]y=-\frac{1}{4}x-6[/tex]
It is required to write the equation of the line parallel to the given line and pass through the point ( 12 , 4 )
The general equation of the line in slope - intercept form is :
[tex]y=m\cdot x+b[/tex]
Where m is the slope and b is y - intercept
As the line are parallel , so, the slope of the required line will be equal to the slope of the given line
So, the slope = m = -1/4
So, the equation of the line will be :
[tex]y=-\frac{1}{4}x+b[/tex]
Using the given point ( 12 , 4 ) to find b
so, when x = 12 , y = 4
[tex]\begin{gathered} 4=-\frac{1}{4}\cdot12+b \\ \\ 4=-3+b \\ 4+3=b \\ b=7 \end{gathered}[/tex]
So, the equation of the required line is :
[tex]y=-\frac{1}{4}x+7[/tex]
