anonymous
  • anonymous
what is the equation of the line parallel to the line y = 2x + 3 that passes through the point 1,4 in slope intercept form?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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anonymous
  • anonymous
@jim_thompson5910
jim_thompson5910
  • jim_thompson5910
what is the slope of the given line
anonymous
  • anonymous
?

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jim_thompson5910
  • jim_thompson5910
what is the equation of the given line
anonymous
  • anonymous
y = 2x+3?
jim_thompson5910
  • jim_thompson5910
what is the slope of that line
jim_thompson5910
  • jim_thompson5910
hint: y = mx+b has a slope of m
anonymous
  • anonymous
I have no idea.. do I input something?
jim_thompson5910
  • jim_thompson5910
in y = 2x+3, what is the number in front of the x variable?
anonymous
  • anonymous
2
jim_thompson5910
  • jim_thompson5910
so that is the slope
jim_thompson5910
  • jim_thompson5910
any line parallel to y = 2x+3 will also have a slope of 2
jim_thompson5910
  • jim_thompson5910
since parallel lines have equal slopes
anonymous
  • anonymous
Right.. but how do I figure out the equation?
jim_thompson5910
  • jim_thompson5910
how would you find the equation of the line if you knew the slope and a point that goes through it?
anonymous
  • anonymous
I don't remember this at all
jim_thompson5910
  • jim_thompson5910
we know that m = 2 we also know that x = 1 and y = 4 since we have the point (1,4) on this parallel line
jim_thompson5910
  • jim_thompson5910
so... y = mx+b y = 2x + b ... plug in m = 2 4 = 2*1 + b ... plug in x = 1 and y = 4 solve for b
anonymous
  • anonymous
Oh so you plug it in.. okay. 4 = b + 2
jim_thompson5910
  • jim_thompson5910
which means b = ???
anonymous
  • anonymous
2?
jim_thompson5910
  • jim_thompson5910
good, the equation of the parallel line is y = 2x + 2
anonymous
  • anonymous
Can we do one other for practice?
jim_thompson5910
  • jim_thompson5910
sure
anonymous
  • anonymous
One sec.. so... What is the equation of the line perpendicular to the line y = 2x + 3 that passes through the point (1,4) in point-slope form? Would we use the same formula?
jim_thompson5910
  • jim_thompson5910
it's a bit different with perpendicular lines
jim_thompson5910
  • jim_thompson5910
the given slope is 2, which is really 2/1 flip the fraction: 2/1 -----> 1/2 flip the sign: 1/2 ----> -1/2
jim_thompson5910
  • jim_thompson5910
so the perpendicular slope is -1/2
jim_thompson5910
  • jim_thompson5910
so we know that m = -1/2 x = 1 y = 4 plug them all into y = mx + b then solve for b
anonymous
  • anonymous
4 = -1/2(1) + b b = 9/2 would it be... y - 4 = -1/2(x-1)?
jim_thompson5910
  • jim_thompson5910
you could use point slope form now get it into slope intercept form
jim_thompson5910
  • jim_thompson5910
oh i see what you mean
jim_thompson5910
  • jim_thompson5910
you got b = 9/2, so the equation in slope intercept form is \[\large y = -\frac{1}{2}x + \frac{9}{2}\]
jim_thompson5910
  • jim_thompson5910
you could write it in point slope form to get y - 4 = -1/2(x-1)
anonymous
  • anonymous
so I could use that solution?
jim_thompson5910
  • jim_thompson5910
either one works, it will depend on what your book or teacher wants
anonymous
  • anonymous
Yeah, I think the second one is what she wants. Thanks again. :)
jim_thompson5910
  • jim_thompson5910
you're welcome

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