Question

Write a linear equation that contains the ordered pair shown in the table below:

y = -2x + 1

y = 2x + 1

y = 2x - 1

y = -2x -1

Answer 1

`y=2x-4`

Explanation:

Let the equation of line is
`y=mx+b`, where
`m` is the slope of the line.

It passes through
`(-5,-14),(-2,-8)\ and\ (1,-2)`.

(Slope of the line joining
`(x_1,y_1)\ and\ (x_2,y_2)=(y_2-y_1)/(x_2-x_1)`)

Hence slope of the given line

`m=(-8(-14))/(-2-(-5))=(-8+14)/(-2+5)=(6)/(3)=2`

Equation of line is:
`y=2x+b`

The line passes through
`(1,-2)`

`-2=2* 1+b\\b=-2-2\\b=-4`

Check if
`(-5,-14)` is on the line
`y=2x-4`

`L.H.S.=-14\\R.H.S.=2* (-5)-4=-10-4=-14\\L.H.S.=R.H.S.`

Hence line passes through
`(5,-14)`.

Check if
`(-2,-8)` is on the line
`y=2x-4`

`L.H.S.=-8\\R.H.S.=2* (-2)-4=-4-4=-8\\L.H.S.=R.H.S.`

Hence line passes through
`(-2,-8)`.