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 line parallel to y = -5x + 6 and passes through the point (-4, -1) is y = -5x -21

Solution:

Given that, a line passes through (-4, -1) and it is parallel to y = -5x + 6

We have to find the line equation of that line.

Now, as we can see given line equation is in slope intercept form y = mx + c

where "m" is the slope of line and "c" is the y-intercept

So, by comparison, slope of that line is m = -5

We know that slopes of two parallel lines are equal

And as the required line is parallel to given line, it will also have the same slope.

Then, slope of our line = -5

And let us find the line equation point slope form

y – a = m(x - b) where (b, a) is a point on the line

So, line equation is y – (-1) = -5(x – (-4))

y + 1 = -5(x + 4)  

y + 1 = -5x – 20  

y = -5x -20 – 1

y = -5x -21

Thus the equation of required line is y = -5x -21