Question

Find the equation of the line passing through the points (-1,-2) (-2,7)

Answer 1

The slope-intercept form of a line:

`y=mx+b`

m - slope

b - y-intercept.

The formula of a slope:

`m=(y_2-y_1)/(x_2-x_1)`

We have the points (-1, -2) and (-2, 7). Substitute:

`m=(7-(-2))/(-2-(-1))=(9)/(-1)=-9`

Therefore we have
`y=-9x+b`.

Put the coordinates of the point (-1, -2) to the equation of a line:

`-2=(-9)(-1)+b`

`-2=9+b` subtract 9 from both sides

`-11=b\to b=-11`

Answer: y = -9x - 11