Question

PLEASE ANSWER FAST !!!!!!!!!!!!!!

A line passes through (3, 7) and (6, 9). Which equation best represents the line?

y = 3 over 2x + 5
y = 2 over 3x + 5
y = 3x + 2
y = 2 over 3x + 2

Answer 1

B.
`y = (2)/(3) x + 5`

Explanation:

Let's use the slope equation first. The slope equation is as follows:

`(y2-y1)/(x2-x1) = slope`

This is what is given in the equation:

• Point (3,7)
• Point (6,9)

Let's label each component of the equation using these points:

y2 = 9

y1 = 7

x2 = 6

x1 = 3

Now, plug these into the equation

`(9-7)/(6-3) = (2)/(3)`

We can now eliminate A and C of the answer choices.

Now let's find the y intercept

Right now we have the following equation

`y = (2)/(3) x+ (y intercept)`

In order to find the y intercept we need to plug in one of the given points into the equation. Let's use point (3,7).

The equation should look like this now:

`7 = (2)/(3)(3) + (yintercept)`

Now lets solve for the y-intercept

`7 = (2)/(3)(3) + (yintercept)\\7 = (6)/(3) + (yintercept)\\7 = 2 + (yintercept) \\5 = yintercept`

Now that we found the y-intercept is 5 we have our full equation!

`y = (2)/(3) x + 5`

Hope this helps!!

- Kay