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# coordinates

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Line a is parallel to line b and goes through the point (1,2). Line b goes through the point (8,1) and is perpendicular to line c whose equation is y=-2x+3. Find the y-intercept of line a.

Jul 10, 2023

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Lets begin with the problem by find the slope of line b.

We know that if a line is perpendicular to another line the its slope hase an opposite sine (+ turns to -), and its the recipricol of it.

So, based of this piece of knowledge we know that the slope of line c is \(-2\), so the slope of line b is \(1/2\).

With this piece of info we can easily find the slope of line a!

Parallel lines have equal slope so now we know the slope of line a is \(1/2\) as well!!

Now lets find the equation of line a using point-slope form!

Point-Slope Form: y=m(x-x1)+y1

We know it goes through the point \((1,2)\) so we can use this as our point, and we can use \(1/2\) as our slope!
Now we have the equation of line a!:

\(y=1/2(x-1) +2\)

\(y=1/2x+3/2\)

Great! But, this isn't our answer, but... we can use this equation to find our answer!!
To find the y-intercept of a certain line, we must replace x with \(0 \)! That's super easy!

\(y = 1/2(0)+3/2\)
\(y = 3/2\)