Question

Write the equation of the line that passes through (4,2) and is parallel to the line y=2x-1

Answer 1

Answer: y = 2x-6

Step-by-step explanation:

So we need to write the equation of a line parallel to y=2x-1.

In parallel lines, the slope is the same, so in our new line the slope will be 2x.

We have the equation y = 2x right now. Let's plug in (4,2) for (x,y) and see if it works out, since it must pass through that point.  

y = 2x

2 = 2 * 4

2 doesn't equal 8.  

But if we subtract 6 from the right side of the equation -

y = 2x-6

then it checks out

2 = 2 (4) - 6

2 = 8 - 6

2 = 2

Answer 2

Answer: y=2x-6

Let’s first rewrite the equation given

y=2x-1

we know that the equation we need to make is parallel to this, which tells us that it will have the same slope.

Our new equation so far is:

y=2x+b

This is because we know the slope, but not the y-intercept. Let’s find this now but substituting the point into this equation

2=2(4)+b

*multiply 2 and 4*

2=8+b

*subtract 8 on both sides*

2=8+b
-8 -8
_____
-6=b

Let’s substitute this into where we had b previously, and finish our equation

y=2x-6

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