Given Information
y−2x=3 need to find a perpendicular line to this line that passes through the point (2,5)
For starters, solve for y in the first equation.
y−2x=3
y=2x+3
Now that we have the equation that is easy to read, to make a line perpendicular, the slope is ALWAYS the reciprocal. So the slope in this equation is 2x. The reciprocal, which is the absolute opposite in sign and numbers (flipping up side down as some call it), would be −12x. So if you were to graph the lines
y=2x+3 and y=−12x+3 they would be perpendicular. However, we are not done yet, since we need to get it through the point (2,5).
Doing this, you need to use the equation y−h=m(x−k). Your teacher may have used this equation, but with different variables.
yandx will be staying the same so the only variables you need to worry about would be h,m,andk.
h will the the y coordinate of the point you want it to pass through, in this case, that would be 5, since in (2,5), 5 is the y coordinate.
m will be the slope, we already calculated that as it's the reciprocal, so it'll be −12.
k is the x coordinate of the point. In (2,5), the x coordinate is 2.
So there you have it! Just plug in the known information in the equation.
y−h=m(x−k) Equation
y−(5)=−12(x−2)
y−(5)=−12x+1 || Distributed the −12 to the x and −2 term.
y=−12x+6 Added the 5 from the left side.
