Respuesta :
Answer:
The points (4,11), (6,14), (30,50) lie on the line joining the points (0,5) and (2,8).
Step-by-step explanation:
The equation of the line passing through two points [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] is
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]
So, the equation of the line passing through two points (0,5) and ( 2, 8 ) is
[tex]y-5=\frac{8-5}{2-0}(x-0)[/tex]
[tex]\Rightarrow y=1.5x+5\cdots(i)[/tex]
For the point (4,11), pout x=4 in equation (i), we have
[tex]y=1.5\times4 +5=11[/tex], which is given y coordinate, hence this point (4,11) lies on the line.
For the point (5,10), pout x=5 in equation (i), we have
[tex]y=1.5\times5 +5=12.5,[/tex] which is not the given y coordinate, hence the point (5,10) doesn't lie on the line.
For the point (6,14), pout x=6 in equation (i), we have
[tex]y=1.5\times6 +5=14[/tex], which is the given y coordinate, hence the point (6,14) lies on the line.
For the point (30,50), pout x=30 in equation (i), we have
[tex]y=1.5\times30 +5=50[/tex], which is the given y coordinate, hence the point (30,50) lies on the line.
For the point (40,60), pout x=40 in equation (i), we have
[tex]y=1.5\times40 +5=65[/tex], which is not the given y coordinate, hence the point (40,60) doesn't lie on the line.
Hence, the points (4,11), (6,14), (30,50) lie on the line joining the points (0,5) and (2,8).
