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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

User Nebu
by
8.4k points

1 Answer

3 votes

Answer:

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

User Gztomas
by
8.3k points

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