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

User Slinkp
by
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1 Answer

17 votes
17 votes

Answer:


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!

User Genish Parvadia
by
2.7k points
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