Write an equation for the line that is parallel to the given line and that passes through the given point.

y = 2x+ 7; (3, 11)
how would you solve this?? how would the y intercept change and how does the point affect this?

Question

Write an equation for the line that is parallel to the given line and that passes through the given point.

y = 2x+ 7; (3, 11)
how would you solve this?? how would the y intercept change and how does the point affect this?

shadowlegendx · Answer

Do you know what a parallel line is?

lxdrpr · Answer

yes so far i have y=2x but idk how the y intercept would change

lxdrpr · Answer

the slope remains the same ik that

shadowlegendx · Answer

Yes, so we know that the slope of this new line will be 2x, but we also know that it must pass through (3,11).

So we must determine the y intercept. This requires a little, head work.

Our line rises by 2 units and runs by 1 unit
2/1

So wherever it intercepts along the y axis, it would have to eventually reach (3,11)

I can determine the y intercept, by bringing subtracting 1 unit from (3,11) for the run, and 2 units from 11 for the rise. I get (2,9). Repeat, (1,7). Repeat (0, 5)

shadowlegendx · Answer

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lxdrpr · Answer

ok so you remove the units until the y intercept is the one found 
so it would be y=2x+5

shadowlegendx · Answer

Yes, as it's parallel to y = 2x + 7 and will eventually reach (3,11) on the graph

lxdrpr · Answer

ok thank you!

shadowlegendx · Answer

No problem

shadowlegendx · Answer

My way is a little unorthodox, so just so you have the formal way to refer to...

Point Slope Formula:

$$y - y _{1} = m(x - x _{1})$$

Where,
m = slope
x1 and y1 = any point

In this problem,
m = 2x
Point = (3,11)

Input

$$y - 11 = 2(x - 3)$$

Distribute 2

$$y - 11 = 2x - 6$$

Add 11 to both sides

$$y = 2x + 5$$