Question

Find an equation of the line passing through the point A(4,7) and perpendicular to the line through points B(-1,-2) and C(5,8).

Answer 1

Answer:

The equation of line is $y=-0.6x+9.4$

Step-by-step explanation:

Since the line is perpendicular to the line passing through (-1,-2) and (5,8) the product of it's slope and the line is related as

$m_{1}\times m_{2}=-1$

Slope of line  through (-1,-2) and (5,8) is

$m_{2}=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}=\frac{8-(-2)}{5-(-1)}\\\\\therefore m_{2}=\frac{10}{6}\\\\Now,\\\\m_{1}\times m_{2}=-1\\\\\therefore m_{1}=\frac{-1}{\frac{10}{6}}=\frac{-6}{10}=-0.6$

Now we know that general equation of line is given by

$y=m_{1}x+c$

Applying value we get

$y=-0.6x+c$

The value of 'c' can be obtained as we know that the line is passing through (4,7)

Thus we have

$7=-0.6\times 4+c\\\\\therefore c=9.4\\\\\therefore y=-0.6x+9.4$