Answer :
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]).