Question

15 points

Line AB←→ passes through the points A(3,−1) and B(1,7).

Which lines are parallel to AB←→?

THIS IS MULTIPLE CHOICES
y=−4x
y=−4x+8
y=4x
y−1=2(x+2)
y+1=−4(x+1)
y=4x+7
y=2x−3
y−6=−4(x−3)

Answer 1

Lines that are parrellell presume to have the same slope.

So if we just calculate the slope of a function or a line we should be good.

`s=\frac{\Delta{y}}{\Delta{x}}=(y_2-y_1)/(x_2-x_1)`

Now put in the data from the coordinates of the points
`A(3,-1)\wedge B(1,7)`

`s=(7-(-1))/(1-3)=(8)/(-2)=\underline{-4}`

The form of a function now looks like:
`</p><p>f(x)\vee y=-4x+n`

From here we are no longer required to calculate anything more. Leave n alone.

The solutions are the equations of the form above.

That would mean:

`</p><p>y=-4x \\</p><p>y=-4x+8 \\</p><p>y+1=-4(x+1) \\</p><p>y-6=-4(x-3)</p><p>`

Hope this helps.