Write an equation for the line that is parallel to y = 2x + 6 and passes through (-1,5).

y=2x+7

Step-by-step explanation:

A linear equation is typically organized in the form y=mx+b, where m is the slope of the line and b is the y-intercept (the y-coordinate of the point on the line that crosses the y-axis).

Parallel lines always have the same slope. When we examine the given equation, y=2x+6, we can identify immediately that 2 is in the place of m, the slope. This means that the slope of the line we're trying to solve for is also 2. So far, our equation looks like this:

y=2x+b

The last thing we need to calculate is b, the y-intercept. We can do this by plugging in the given point (-1,5) as x and y.

y=2x+b

5=2(-1)+b

5=-2+b

Add 2 to both sides to isolate b

5+2=-2+b+2

7=b

Now that we know b, we plug that into our original equation and now we have a final equation of:

y=2x+7

I hope this helps!

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