Write an equation of the line passing through each of the following pairs of points. a (−10, 4), (2, −5)

Answer:see explanationStep-by-step explanation:The equation of a line in slope- intercept form isy = mx + c ( m is the slope and c the y- intercept )Calculate m using the slope formulam = (y₂ - y₁ ) / (x₂ - x₁ )with (x₁, y₁ ) = (- 10, 4) and (x₂, y₂ ) = (2, - 5)m = [tex]\frac{-5-4}{2+10}[/tex] = [tex]\frac{-9}{12}[/tex] = - [tex]\frac{3}{4}[/tex], thusy = - [tex]\frac{3}{4}[/tex] x + c ← is the partial equation of the lineTo find c substitute either of the 2 given points into the partial equationUsing (2, - 5), then- 5 = - [tex]\frac{3}{2}[/tex] + c ⇒ c = - 5 + [tex]\frac{3}{2}[/tex] = - [tex]\frac{7}{2}[/tex]y = - [tex]\frac{3}{4}[/tex] x - [tex]\frac{7}{2}[/tex] ← equation of line