Answer: d=9.
Step-by-step explanation:
(2,5) (-3,1) (7,d) d=?
Line equation
[tex]\displaystile\\\boxed {\frac{x-x_1}{x_2-x_1}=\frac{y-y_1}{y_2-y_1} }[/tex]
x₁=2 x₂=-3 y₁=5 y₂=1
[tex]\displaystyle\\\frac{x-2}{-3-2} =\frac{y-5}{1-5} \\\\\frac{x-2}{-5} =\frac{y-5}{-4} \\[/tex]
Multiply both parts of the equation by -20:
[tex]4*(x-2)=5*(y-5)\\4x-8=5y-25\\4x-8+25=5y-25+25\\4x+17=5y\\[/tex]
Multiply both parts of the equation by 5:
[tex]0,8x+3,4=y\ \ \ \ (1)[/tex]
Let us substitute the coordinate (7,d) into equation (1):
[tex]0,8*7+3,4=d\\5,6+3,4=d\\9=d[/tex]
