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Question 558554: Find (a)the equation of the line that is parallel to the given line and includes the given point, and (b) the equation of a line that is perpendicular to the given line through the given point. Wright both answers in slope-intercept form. (c) Graph both of these lines on the same axes. Please show all of your work.
y=-x+4,(-3,7)
Answer by solver91311(24713)   (Show Source):
You can put this solution on YOUR website!
Parallel lines have equal slopes. Perpendicular lines have slopes that are negative reciprocals.
For your part a) note that the given point is on the given line. Therefore the desired equation is identical to the given equation.
For your part b) calculate the negative reciprocal of the slope of the given line, then used the point slope form of an equation of a line to derive the desired equation.
 )
where ) are the coordinates of the given point and  is the given/calculated slope.
Rearrange to put the equation into slope-intercept form, that is:  .
For your graphs, you already have one point on each of your lines, namely the given point, so plot that point. Select a small integer value for  , substitute that value for into one of your equations, calculate the value of  that results, create the point ) from the value you selected for and the value you calculated for , then plot the point. Draw a line through the two points. Repeat for the other equation.
John
My calculator said it, I believe it, that settles it
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