Answer:
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 [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
Slope of a line passing through (-2, 12) and (3, -23) = [tex]\frac{12+23}{-2-3}[/tex] = (-7)
Option (1)
Slope of a line passing through (-4, 17) and (5, -28) = [tex]\frac{17+28}{-4-5}[/tex] = (-5)
Option (2)
Slope of a line passing through (-2, 16) and (2, -20) = [tex]\frac{16+20}{-2-2}[/tex] = (-9)
Option (3)
Slope of a line passing through (-6, 14) and (4, -16) = [tex]\frac{14+16}{-6-4}[/tex] = (-3)
Option (4)
Slope of a line passing through (-3, 19) and (6, -44) = [tex]\frac{19+44}{-3-6}[/tex] = (-7)
Option (5)
Slope of a line passing through (-5, 32) and (3, -24) = [tex]\frac{32+24}{-5-3}[/tex] = (-7)
Slopes of options (1), (2) and (3) are different.
Therefore, Options (1), (2) and (3) will be the correct options.
