Question

8. Parallel to the line y = 2x + 5 and contains the

point (4, 5) in slope-intercept form.
Please help and show work .

Answer 1

`y=2x-3`

Explanation:

So we want to find an equation in slope-intercept form that is parallel to:

`y=2x+5`

And contains the point (4,5).

So to create the equation, we will need to slope and the y-intercept.

First, recall that parallel lines have the same slope. Since we want our equation to be parallel to y=2x+5, this means that the slope of the new equation must be 2.

Now, we can use the point-slope form to solve for the y-intercept. The point slope form is:

`y-y_1=m(x-x_1)`

Let (4,5) be x₁ and y₁. m is 2 since it's parallel to y=2x+5. Thus:

`y-5=2(x-4)\\`

Distribute:

`y-5=2x-8`

Add 5 to both sides:

`y=2x-3`

And that's our equation :)