Question

Find an equation relating x and y

Answer 1

(3,3) is a 3rd of (6,9)

Explanation:

Answer 2

The equation of the line passing through the points (3,3) and (6,9), and also through the point (x, y), is
`\(y = 2x - 3\)`.

To find the equation of the straight line passing through the points (3,3) and (6,9), we can use the slope-intercept form of a line, which is given by:

`\[ y = mx + b \]`

where
`\(m\)` is the slope and
`\(b\)` is the y-intercept.

First, calculate the slope
`(\(m\))` using the formula:

`\[ m = \frac{{y_2 - y_1}}{{x_2 - x_1}} \]`

Let
`\((x_1, y_1) = (3,3)\) and \((x_2, y_2) = (6,9)\)`:

`\[ m = \frac{{9 - 3}}{{6 - 3}} = (6)/(3) = 2 \]`

Now that we have the slope
`(\(m\))`, we can use one of the points, say
`\((3,3)\)`, to find the y-intercept
`(\(b\))`. Plug the values into the equation:

`\[ 3 = 2(3) + b \]`

Solving for
`\(b\)`:

`\[ 3 = 6 + b \]`

`\[ b = 3 - 6 = -3 \]`

Now, we have the slope
`(\(m\))` and the y-intercept
`(\(b\))`. The equation of the line is:

`\[ y = 2x - 3 \]`

Now, the line also passes through the point
`\((x, y)\)`. Since this point lies on the line, we can substitute
`\(x\)` and
`\(y\)` into the equation:

`\[ y = 2x - 3 \]`

This is the equation relating
`\(x\)` and
`\(y\)` for the line passing through the points (3,3) and (6,9), as well as the additional point (x, y).

The question probable maybe:

All three points displayed are on the line. Find an equation relating x and y.