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

a. (13,y)
$y=-\frac{1}{2} \times 13+6 \\ y=-\frac{13}{2}+6 \\ y=-6.5+6 \\ y=-0.5 \\ \\ \boxed{(13,-0.5)}$

b. (x,7.75)
$7.75=-\frac{1}{2}x + 6 \\ 7.75 -6=-\frac{1}{2}x \\ 1.75=-\frac{1}{2}x \\ 1.75 \times (-2)=x \\ x=-3.5 \\ \\ \boxed{(-3.5,7.75)}$