Please help! Don't understand how to do these and have a midterm coming up :( Will give medal and fan for explanations. TIA given the line with equation y=2x+9, find a.) the line parallel to the given line that passes through (7, -1) b.) a line perpendicular to the given line that passes through (8, 5) c.) the point of intersection for the lines with the equation: 3x-5y=13 and 7x+2y=3
For a) Question: what is the slope of the given line?
2?
yup, so the slope of the required line, ( which is parallel to the given line), is 2 also, right?
yes!
so, with slope m =2, point (7,-1) , you can write the equation of it, right? (y = mx +b)
so would it just be like y=2x-1? I feel like I'm completely wrong
nope!! y = mx + b you need b, so - mx both sides b = y - mx replace y = -1, m =2, x =7, you have b = -1-2(7) = -15 replace back y = mx + b, you have y = 2x -15 is the required line.
Ohh okay that makes sense!
For b) the required line is perpendicular to the given line, hence, its slope = \(-\dfrac{1}{2}\) Do the same with part a) to get the answer.
Okay. So it would be y=-1/2x+9?
yup
for c) just solve the system by elimination or substitution.
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