a line has a slope of -2/3 for a pair of points on the line. Find the missing coordinate if the points are (-1,y) and (4,7)

Answer:The missing co-ordinate is: (-1,[tex]$ \frac{31}{3} $[/tex]).Step-by-step explanation:Given the slope of a line and a point on it, we determine the equation of the line by slope - one point form. Slope - one point form: (y - y₁) = m(x - x₁)Where, (x₁,y₁) is the point passing through the line.Here the slope is [tex]$ \frac{-2}{3} $[/tex] and the point (x₁,y₁) = (4,7).Therefore the equation would be: y - 7 = [tex]$ \frac{-2}{3} $[/tex](x - 4)⇒  3y - 21 = -2x + 8⇒                       2x + 3y - 29 = 0       is the equation of the line.Now it is given that (-1,y) also passes through the line, this point should satisfy the equation.⇒ 2(-1) +3y = 29⇒ 3y = 31  i.e., y = [tex]$ \frac{31}{3} $[/tex]Therefore, the missing co-ordinate is:   (-1,[tex]$ \frac{31}{3} $[/tex]).