Question

Find the equation of line passing througgh (-3,5) and perpendicular to the line through the points (2,5) and(-3,6)

Answer 1

Answer:

y=5x+$\frac{22}{5}$

Step-by-step explanation:

The equation of the line through the points (2,5) and (-3,6) is y=$\frac{-1}{5}$x+$5\frac{2}{5}$.

The slope of this line is equal to $\frac{-1}{5}$.

We know that a line is perpendicular to another line if the two slopes are opposite reciprocals of one another.

The opposite reciprocal of $\frac{-1}{5}$ is 5.

So the new equation is y=5x+b

To find what b is, plug in (-3,5) to the equation so

5=$\frac{-1}{5}$·(-3)+b

And simplify.

5=$\frac{3}{5}$+b

5-$\frac{3}{5}$=b

b=$\frac{22}{5}$

And put b back into the equation:

y=5x+$\frac{22}{5}$