Question

A line passes through the points (6,3) and (-4,8). The line also passes through the following points. Calculate the missing co-ordinate.

a. (13,y) b.(x, 7.75)

Answer 1

Find the equation of the line:

`(6,3) \\ x_1=6 \\ y_1=3 \\ \\ (-4,8) \\ x_2=-4 \\ y_2=8 \\ \\ m=(y_2-y_1)/(x_2-x_1)=(8-3)/(-4-6)=(5)/(-10)=-(1)/(2) \\ \Downarrow \\ y=\frac-{1}{2}x+b \\ \\ (6,3) \\ 3=-(1)/(2) * 6+b \\ 3=-3+b \\ 3+3=b \\ b=6 \\ \\ \hbox{the equation:} \\ y=-(1)/(2)x+6`

a. (13,y)

`y=-(1)/(2) * 13+6 \\ y=-(13)/(2)+6 \\ y=-6.5+6 \\ y=-0.5 \\ \\ \boxed{(13,-0.5)}`

b. (x,7.75)

`7.75=-(1)/(2)x + 6 \\ 7.75 -6=-(1)/(2)x \\ 1.75=-(1)/(2)x \\ 1.75 * (-2)=x \\ x=-3.5 \\ \\ \boxed{(-3.5,7.75)}`