Question

Find an equation of the line that pases (8,17) and is perpendicular to the line x+2y=2

Answer 1

y = 2x + 1

Explanation:

The equation of line is given in this format:

y = mx + b

Where m is the slope and b is the y-intercept

Now, let's take this equation and put it in this format:

`x+2y=2\\2y=-x+2\\y=-(1)/(2)x+1`

Line perpendicular to this will have slope that is "negative reciprocal" of this. Which means that it will be "flipped" and negative of this line's slope.

The slope of this line is
`-(1)/(2)` and thus perpendicular line has slope 2

So perpendicular line will have equation:

y = mx + b

y = 2x + b

Passes through the point (8,17), so we plug in x = 8 and y = 17 and get b:

`y = 2x + b\\17=2(8)+b\\17=16+b\\b=17-16\\b=1`

So, the equation is:

y = 2x + 1