Question

Someone please help me with this question??

Examine the following table that represents some points on a line.
Which equations in point-slope form represents this line?

y + 10 = 2(x + 6)

y + 9 = 1/2(x + 4)

y + 10 = 1/2(x + 6)

y + 4 = 1/2(x — 6)

y + 4 = 2 (x — 6)

y — 9 = 2(x — 4)

Answer 1

Option (2), (3) and (4)

Explanation:

Let the equation of the line representing the given table is,

y - y' = m(x - x')

where 'm' = slope of the line

(x', y') is the point lying on the line.

Let the two points (-6, -10) and (-4, -9) lie on the line

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

=
`(-9+10)/(-4+6)`

=
`(1)/(2)`

Equation of the line passing through (-4, -9) with slope
`(1)/(2)` will be

y - (-9) =
`(1)/(2)(x+4)`

y + 9 =
`(1)/(2)(x+4)`

Equation of the line passing through (-6, -10) with slope =
`(1)/(2)`

y - (-10) =
`(1)/(2)(x+6)`

y + 10 =
`(1)/(2)(x+6)`

Equation of the line passing through (6, -4) and slope =
`(1)/(2)`

y + 4 =
`(1)/(2)(x-6)`

Therefore, Options (2), (3) and (4) will be the answer.