the line passing through the points (-2,12) and (3, -23) intersects the line passing through which of these pairs of points

Options (1), (2) and (3)

Step-by-step explanation:

To solve this problem we will use the property,

"A system of equations will have a unique solution if slopes of the linear equations are different"

Slope of a line passing through two points and =

Slope of a line passing through (-2, 12) and (3, -23) = = (-7)

Option (1)

Slope of a line passing through (-4, 17) and (5, -28) = = (-5)

Option (2)

Slope of a line passing through (-2, 16) and (2, -20) = = (-9)

Option (3)

Slope of a line passing through (-6, 14) and (4, -16) = = (-3)

Option (4)

Slope of a line passing through (-3, 19) and (6, -44) = = (-7)

Option (5)

Slope of a line passing through (-5, 32) and (3, -24) = = (-7)

Slopes of options (1), (2) and (3) are different.

Therefore, Options (1), (2) and (3) will be the correct options.