The slope of parallel lines is the same. For the line y = -4x + 3, which is in slope-intercept form, the slope is -4.
The line passing through the point (3, 6) should also have a slope of -4.
The equation of this line is given by (y - 6)/(x - 3) = -4
=> y - 6 = -4x + 12
=> y = -4x + 18
The equation of the line passing through (3, 6) and parallel to the line y = -4x + 3 is y = -4x + 18
Slope-intercept form is y = mx + b
where: m=slope & b=y-intercept
The slope of the line // to y = -4x+3 is -4, if this line passes (3, 6) then
6 = -4(3) + b
again by slope-intercept form,
y = -4x + 18....eq. of // line to y =-4x+3
y= -4x + 3
we can write above equation as 4x+y=3
Parallel line to the above line is 4x+y=k
but this line is passing (3,6).
So the parallel line is 4x+y=18 ,we can the line as y=-4x+18