Question

Find the equation of the line that passes through (1,3) and is perpendicular to y = 1 − 2 x

Answer 1

`y=\displaystyle(1)/(2) x+\displaystyle (5)/(2)`

Explanation:

Hi there!

Linear equations are typically organized in slope-intercept form:
`y=mx+b` where m is the slope and b is the y-intercept.

Perpendicular lines always have slopes that are negative reciprocals (ex. 1/2 and -2, 3/4 and -4/3)

Determine the slope (m):

`y = 1 -2x`

Rearrange into slope-intercept form:

`y = -2x+1`

Now, we can identify clearly that the slope is -2. Because perpendicular lines always have slopes that are negative reciprocals, a perpendicular line would have a slope of
`\displaystyle(1)/(2)`. Plug this into
`y=mx+b`:

`y=\displaystyle(1)/(2) x+b`

Determine the y-intercept (b):

`y=\displaystyle(1)/(2) x+b`

Plug in the given point (1,3) and solve for b:

`3=\displaystyle(1)/(2) *1+b\\\\b=\displaystyle (5)/(2)`

Therefore, the y-intercept is
`\displaystyle (5)/(2)`. Plug this back into
`y=\displaystyle(1)/(2) x+b`:

`y=\displaystyle(1)/(2) x+\displaystyle (5)/(2)`

I hope this helps!