Answer:
Therefore [tex]m_{2}[/tex] = -3.
Step-by-step explanation:
i) let us say the slope of the line passing through (-2,7) and (4,9) is [tex]m_{1}[/tex].
ii) to find the slope of the line passing through two points ([tex]x_{1}[/tex], [tex]y_{1}[/tex]) and ([tex]x_{2}[/tex],[tex]y_{2}[/tex]) we use the formula m = [tex]\dfrac{y_{2} - y_{1} }{x_{2} - x_{1} }[/tex]. Therefore we can say that [tex]m_{1}[/tex] = [tex]\dfrac{9 - 7}{4 - (-2)}[/tex] = [tex]\dfrac{1}{3}[/tex].
iii) let us say the slope of the perpendicular line to the line passing through (-2,7) and (4,9) is [tex]m_{2}[/tex]
iv) from the formula for the slopes of a line and the line perpendicular to it which is given by [tex]m_{1}[/tex] × [tex]m_{2}[/tex] = -1, therefore [tex]m_{2}[/tex] = -1 ÷ [tex]m_{1}[/tex] = -3. Therefore [tex]m_{2}[/tex] = -3
