Question

Which equation represents a line that passes through (–9, –3) and has a slope of –6?

Answer 1

Slope-poitn form:
We need a point (x₀,y₀) and the slope (m).

y-y₀=m(x-x₀)

In this case:
(-9,-3)
m=-6

y+3=-6(x+9)
y+3=-6x-54
y=-6x-54-3
y=-6x-57

Answer: y=-6x-57

Answer 2

Answer: The required equation of the line is
`6x+y+57=0.`

Step-by-step explanation: We are given to find the equation that represents a line passing through the point (-9, -3) and has a slope of -3.

We know the following point-slope form :

Point-slope form : The equation of a line passing through the point (a, b) and having a slope of m is given by

`y-b=m(x-a).`

For the given line, we have

(a, b) = (-9, -3) and m = -6.

Therefore, the equation of the line is

`y-b=m(x-a)\\\\\Rightarrow y-(-3)=-6(x-(-9))\\\\\Rightarrow y+3=-6(x+9)\\\\\Rightarrow y+3=-6x-54\\\\\Rightarrow 6x+y+54+3=0\\\\\Rightarrow 6x+y+57=0.`

Thus, the required equation of the line is
`6x+y+57=0.`