Find the equation of the line that passes through (1,2) and is perpendicular to y=2x+3. Leave your answer in the form y=mx+c
1 answer:
Answer:
y = -1/2x + 5/2
Step-by-step explanation:
If two lines are perpendicular to each other, they have opposite slopes.
The first line is y = 2x + 3. Its slope is 2. A line perpendicular to this one will have a slope of -1/2.
Plug this value (-1/2) into your standard point-slope equation of y = mx + b.
y = -1/2x + b
To find b, we want to plug in a value that we know is on this line: in this case, it is (1, 2). Plug in the x and y values into the x and y of the standard equation.
2 = -1/2(1) + b
To find b, multiply the slope and the input of x (1)
2 = -1/2 + b
Now, add 1/2 to both sides to isolate b.
5/2 = b
Plug this into your standard equation.
y = -1/2x + 5/2
This equation is perpendicular to your given equation (y = 2x + 3) and contains point (1, 2)
Hope this helps!
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