Question

Which of the following point-slope form equations could be produced with the points (-1, -2) and (4, -3)?

y + 2 = -1/5(x + 1)


y + 1 = -1/5(x + 1)


y + 2 = 1/5(x - 1)


y - 2 = -1/5(x - 1)

Answer 1

The first option could be produced with the points (-1, -2) and (4, -3)

Explanation:

Step 1:

Assume
`(x_(1), y_(1)) = (-1,-2)` and
`(x_(2), y_(2)) = (4,-3)`. So
`x_(1)=-1, y_(1)=-2` and
`x_(2)=4, y_(2)=-3` .

The point-slope form is
`\left(y-y_(1)\right)=m\left(x-x_(1)\right)`.

Step 2:

First, we need to determine the value of the slope, m to substitute in the equation.

The slope is given by
`m=(y_(2)-y_(1))/(x_(2)-x_(1))`.

`m=(-3-(-2))/(4-(-1)) = (-3+2)/(4+1)= -(1)/(5).`

Step 3:

Substituting m's value in the equation, we get

For
`x_(1)=-1, y_(1)=-2`,
`\left(y-y_(1)\right)=m\left(x-x_(1)\right) = \left(y-(-2)}\right)=-(1)/(5) \left(x-(-1)}\right)`
`=\left(y+2}\right)=-(1)/(5) \left(x+1}\right)`.

For
`x_(2)=4, y_(2)=-3`,
`\left(y-y_(1)\right)=m\left(x-x_(1)\right) = \left(y-(-3)}\right)=-(1)/(5) \left(x-4}\right)`
`=\left(y+3}\right)=-(1)/(5) \left(x-4}\right)`.

The first option matches the calculated value
`\left(y+2}\right)=-(1)/(5) \left(x+1}\right)`.