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

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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