Respuesta :
Answer: The value of x is -5 and the value of y is 5.
Explanation:
The slope of the line is [tex]\frac{2}{3}[/tex] and the point is (-2,5) from which the line line is passing.
If a line is passing through the point [tex](x_1,y_1)[/tex] with slope m, the the equation of line is,
[tex]y-y_1=m(x-x_1)[/tex]
[tex]y-5=\frac{2}{3}(x+2)[/tex]
[tex]3y-15=2x+4[/tex]
[tex]3y-2x=19[/tex] ..... (1)
It is given that the point A(x,3) and B(-2,y) lies on the line. It means it satisfies the equation of the line.
Put y=3 in equation (1).
[tex]3(3)-2x=19[/tex]
[tex]-2x=10[/tex]
[tex]x=-5[/tex]
The value of x is -5.
Put x=-2.
[tex]3y-2(-2)=19[/tex]
[tex]3y+4=19[/tex]
[tex]3y=15[/tex]
[tex]y=5[/tex]
The value of y is 5.
