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

Answer:

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

Step-by-step 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' = $\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

               = $\frac{-9+10}{-4+6}$

               = $\frac{1}{2}$

Equation of the line passing through (-4, -9) with slope $\frac{1}{2}$ will be

y - (-9) = $\frac{1}{2}(x+4)$

y + 9 = $\frac{1}{2}(x+4)$

Equation of the line passing through (-6, -10) with slope = $\frac{1}{2}$

y - (-10) = $\frac{1}{2}(x+6)$

y + 10 = $\frac{1}{2}(x+6)$

Equation of the line passing through (6, -4) and slope =  $\frac{1}{2}$

y + 4 = $\frac{1}{2}(x-6)$

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