The equation of the line that is parallel to y = -5x + 6 and passes through the point (-4, -1) in slope intercept form is y = -5x -21
Given that line passes through the point (-4, -1) and parallel to y = -5x + 6
We have to find the equation of line
Let us first calculate the slope of line having equation as y = -5x + 6
The slope intercept form of line is given as:
y = mx + c ---- eqn 1
where "m" is the slope of line and "c" is the y-intercept
Comparing the given equation of line y = -5x + 6 with slope intercept form y = mx + c,
we get the slope of line "m" = -5
We know that slope of two given parallel lines are always equal
Hence the slope of line which is parallel to line with equation y = -5x + 6 is also -5
Now we have to find the equation of line passing through point (-4, -1) with slope -5
Substitute (x, y) = (-4, -1) and m = -5 in eqn 1 to find "c" intercept
-1 = -5(-4) + c
-1 = 20 + c
c = -21
Substitute c = -21 and m = -5 in eqn 1 to get the equation of line
y = -5x + (-21)
y = -5x -21
Thus the equation of required line is found out as y = -5x -21
