Answer:
[tex]y=2x-3[/tex]
Step-by-step explanation:
So we want to find an equation in slope-intercept form that is parallel to:
[tex]y=2x+5[/tex]
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:
[tex]y-y_1=m(x-x_1)[/tex]
Let (4,5) be x₁ and y₁. m is 2 since it's parallel to y=2x+5. Thus:
[tex]y-5=2(x-4)\\[/tex]
Distribute:
[tex]y-5=2x-8[/tex]
Add 5 to both sides:
[tex]y=2x-3[/tex]
And that's our equation :)
