Question

What is a equation of the line that is parallel to y=-5×+6 and passes through the point (-4,-1)

Answer 1

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

Solution:

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