Question

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

Answer 1

Answer:

$y=2x-3$

Step-by-step 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 :)