Question

My paper says to write equations of the lines through the given point (a) parallel to the given line & (b) perpendicular to the given line!

Point; (2,1) and Line; 4x-2y=3

Answer 1

problem (a)
the slope from a line in the form ax+by=c is m=-a/b; so the line that is parallel to this line has the same slope; in this case we have\[m=\frac{-4}{2}=-2\]now that we have the slope and a point you can use the point-slope formula\[y-x_{1}=m(x-x_{1})\]filling in the formula\[y-1=-2(x-2)\]solve for x (if you want slope-intercept form of the line)\[y=-2x+4+1\]\[y=-2x+5\]is the line parallel and through (2,1)

Answer 2

problem (b)
if a line is perpendicular the slope is the negative reciprocal; in this case\[m=\frac{1}{2}\]now we have a point and the slope as do as before\[y-1=\frac{1}{2}(x-2)\]solving for y\[y=\frac{1}{2}x-1+1\]\[y=\frac{1}{2}x\]is the line through (2,1) and perpendicular o the given line

Answer 3

Yeah, it is! Now for perpendicular, how is that supposed to work?

Answer 4

Oh, nevermind! Thank you very much.

Answer 5

in the first post i wrote solve for x in the last step, but i meant solve for y

Answer 6

Oh, okay! I got it, when I looked at how to do it I figured it out, thank you!

Answer 7

welcome