Question

What equation is graphed in this figure?

y−4=−1/3(x+2)

y−3=1/3(x+1)

y+2=−3(x−1)

y−5=3(x−1)
Number graph ranging from negative four to four on the x and y axes. A line is drawn on the graph that passes through begin ordered pair negative one comma four end ordered pair and begin ordered pair one comma negative two end ordered pair

Answer 1

The third equation:
`y+2=-3(x-1)`

Explanation:

The two points on the line are
`(-1,4)` and
`(1,-2)`.

Slope of the line passing through two points
`(x_(1),y_(1))` and
`(x_(2),y_(2))` is given as:

`m=(y_(2) -y_(1))/ (x_(2) -x_(1))`

Here,
`(x_(1),y_(1))` and
`(x_(2),y_(2))` are
`(-1,4)` and
`(1,-2)`.

Therefore, slope is equal to,
`m=(-2-4 )/ (1-(-1)`

`m=-6/2`

`m=-3`

Now, equation of a straight line with slope m and points
`(x_(1),y_(1))` and
`(x_(2),y_(2))` is given as:

`y-y_(1)=m(x-x_(1))\\y-y_(2)=m(x-x_(2))`

Now, if we use the 2nd form, then
`x_(2)=1,y_(2)=-2`.

So, the equation is given as :

`y-(-2)=-3(x-1)\\y+2=-3(x-1)`