Write the equation of the line that passes through the point (1,3) and is perpendicular to the line y = 1/2x - 1

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Write the equation of the line that passes through the point (1,3) and is perpendicular to the line y = 1/2x - 1

Algebra
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can you tell me the slope of this line ? y = 1/2x - 1 ??
In y = mx + b form, the slope is in the m position...so the slope of this line is 1/2. Do you understand that ??
yes

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but we are looking for a perpendicular slope....and perpendicular slopes have negative reciprocal slopes. All that means is we are going to have to " flip " the slope and change the sign. That is the negative reciprocal. So lets flip the slope and change the sign....1/2....neg reciprocal is -2/1 or just -2. So our perpendicular line needs to have a slope of -2. Do you understand so far ??
Yes. With the slope being -2 do you go to find the y-intercept next?
yes... use y = mx + b slope(m) = -2 (1,3)...x = 1 and y = 3 now we basically sub in our info and solve for b....can you do that ?
In y = mx + b, the b stands for your y intercept
where did you get the (1,3)?
those are your points given in your original question.
do you need help in setting up the equation ?
Ok & Yes.
y = mx + b slope(m) = -2 (1,3)...x = 1 and y = 3 now we sub and find b, the y intercept 3 = -2(1) + b 3 = -2 + b 3 + 2 = b 5 = b have I lost you yet ??
No, i understand what you did there.
so we know out slope (m) is -2 and our y intercept (b) is 5... so your perpendicular line passing through (1,3) is : y = -2x + 5
if you have any questions please ask them now :)
Thank you so much! I actually understand how to do it now? Is it the same working out process with parallel?
not quite....parallel lines will have the same slope. So if you were looking for a parallel line .....your slope would be the same as in the original line....your parallel slope would be 1/2....but for perpendicular, you need negative reciprocal slopes...thats when you flip the slope and change the signs.
Ok now i get you. You keep the same but still do the sub in stuff to still find b..right?
yep ^^...thats right :)
Ok. Thank You! (:
no problem :)

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