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Let's find the slope (m) of line passing through points (3 , -2) and (-2 , 8) :

  • [tex] \dfrac{y_2 - y_1}{x_2 - x_1} [/tex]

  • [tex] \dfrac{ - 2 - 8}{3 - ( - 2)} [/tex]

  • [tex] \dfrac{ - 10}{5} [/tex]

  • [tex] - 2[/tex]

slope (m) = -2

now, let's plug the value of slope (m) and coordinates of point (3 , -2) to find c (y - intercept)

[tex]y = mx + c[/tex]

  • [tex] - 2 = (3 \times - 2) + c[/tex]

  • [tex] - 2 = - 6 + c[/tex]

  • [tex]c = - 2 + 6[/tex]

  • [tex]c = 4[/tex]

Y - intercept of the given line is 4, so the required equation will be :

  • [tex]y = - 2x + 4[/tex]

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