Write the equation of a line that is perpendicular to x=5.
x=5 is a straight line going through 5 on the x axis. A line perpendicual to this will be any line parallel to the x axis. This would mean y=[Any Number]. Pick what you want for [Any Number}, but I'll choose my lucky number, 6.
y =6
Write the equation of a line that is parallel to 4x+3y=1.
A parallel line have the same slope, so we can start by rewriting the equation in standard form of y=mx + b, where m is the slope and b the y-intercept (the value of y when x=0):
3y = -4x + 1
y = -(3/4)x + (1/3)
The slope is -(3/4), so the new line will also have the nsame slope. Start by putting -(3/4) in the satandard format:
y = -(3/4)x + b
In the absence of any other information, we are free to pick whatever value we want for b, as long as it is not 1. I'll choose . . .
y = -(3/4)x + 6
Write the equation of a line that is perpendicular to x-5y=2
As before, rewrite into standard form:
-5y = -x + 2
y = (1/5)x + 2
A perpendicular equation will have a slope that is the negative inverse of the reference line. The negative inverse of (1/5) is -5. Now we have:
y = -5x + b
Since we aren't given any addition information, we can pick any b we want.
y = -5x + 6
See the attached graph.
