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allsm [11]
3 years ago
7

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

rdinate.
a. (13,y) b.(x, 7.75)
Mathematics
1 answer:
Anna [14]3 years ago
5 0
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)}
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