Question

What is the equation of the line with slope `m= -6` that passes through `(-11,3)`?

Answer 1

`y = -6 x -63`

Explanation:

The standard equation of a line is `y = m x + c`, so we get `y = -6 x + c`.

Now, since the line passes through the point, the point has to satisfy the equation of the line. Substitute `(-11,3)` in the equation to get:
`3 = -6 (-11) + c => c = -63`.

Thus, the equation of the line becomes `y = -6 x -63`.

Answer 2

`6x+y+63=0`

Explanation:

SUPPOSE, THE EQUATION OF THE STRAIGHT LINE IS,
`y=mx+c`
where `c` is unknown.
now, in the problem,
`m=-6`
and the line goes through `(-11,3)` point.
now, by passing the equation of the straight line through `(-11,3)` point and putting `m=-6` in the equation, we get,
`3=(-6)(-11)+c`
`or,3=66+c`
`or,c=3-66`
`or,c=-63`
now, by putting `m=-6` and `c=-63` in the first equation, we will get the equation of the straight line.
so, the equation of the straight line is,
`y=-6x-63`
`or,6x+y+63=0`