What is the equation in slope intercept form of the line that passes through the point (6, 4) and is parallel to the line represented by y = 2.5x + 6?

Answer 1

Remember the following:

1. In the slope intercept form of a line (y=mx + b), m is the slope, and b is the y-intercept
2. Two parallel lines have the same slope
3. If you have the slope of a line and a point it passes through, the equation of this line can be expressed using the point-slope form : y-y₁ = m(x-x₁), where (x₁, y₁) is a point on the line and m is the slope

So the slope of the line you're given (y = 5/2x + 6) is 5/2. A line that is parallel to this line has the exact same slope. So now you know that the slope of this line is 5/2, and this line also needs to pass through (6,4). Can you use the point-slope form to write the equation of this line, and then simply and convert to the slope-intercept form?

This is the blueprint. Please schedule some time with me to go over step by step if you still can't figure it out.

Answer 2

Hello Tim, I hope you're doing well.

Here's how I would solve this problem:

You are asked to provide an equation in slope intercept form: y= mx + b.

However, you can use the point-slope form with the information given in the problem:

y - y₁ = m(x - x₁)

With that out of the way, let's get into this problem!! You are told that the new line is parallel to the line:

y = 2.5x + 6

That means that your new line's slope, m, will be 2.5!

So far, that gives us y - y₁ = 2.5(x - x₁)

Now, you may be wondering what y₁ and x₁ are compared to the regular y and x.

y₁ and x₁ are the x and y coordinate in the point they gave you! They gave you (6,4) as the point the new line passes through, and, with coordinates being written as (x₁,y₁), that makes x₁ = 6 and y₁ = 4!

Now, we can update our equation from:

y - y₁ = 2.5(x - x₁) --> y - 4 = 2.5(x - 6)

Let's math it out and finish up!

Distributing the 2.5 through the parentheses, we get:

y - 4 = 2.5x - 15

Finally, we have to isolate y! We can do that by adding 4 to each side, to get:

y= 2.5x - 11

That is your answer: y= 2.5x - 11 !!!



You can check this by plugging x=6 and y=4 into this equation and it'll be equal on both sides! The answer I gave is also in the proper slope intercept form of y = 2.5x - 11 !

Hope that helps! Please let me know if this was helpful or if you're confused on any part of the answer, have a good one!