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What is the equation of the line that passes through point Q and is parallel to line P?​

What is the equation of the line that passes through point Q and is parallel to line-example-1
User Chad Okere
by
7.6k points

1 Answer

4 votes

Answer:


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

Explanation:

What we need to know:

  1. Linear equations are typically organized in slope-intercept form:
    y=mx+b where m is the slope and b is the y-intercept (the value of y when the line crosses the y-axis)
  2. Parallel lines always have the same slope (m) and different y-intercepts (b)

1) Find the slope of line P

The slope of a line is equal to the
(rise)/(run), or the number of units the line moves up over the number of units the line moves to the right.

We can see that for line P, for every 2 units it moves to the right, it moves up 3 units.

Therefore, the slope of line P is
(3)/(2).

Knowing this, the equation of a line parallel to line P would have a slope of
(3)/(2) as well. Plug this into
y=mx+b as m:


y=(3)/(2) x+b

2) Plug the given point Q into
y=(3)/(2) x+b to find the y-intercept (b)


y=(3)/(2) x+b

Plug in point Q (2,4)


4=(3)/(2) (2)+b\\4=(6)/(2)+b\\4=3+b

Subtract 3 from both sides


4-3=3+b-3\\1=b

Therefore, the y-intercept of this line (b) is 1. Plug this back into our original equation:


y=(3)/(2) x+b


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

I hope this helps!

User Erik Lindblad
by
7.4k points

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