find the missing coordinates given the slope (2,x) and (0,8) m=-2

We are given two points, \((2, x)\) and \((0, 8)\), with a slope \(m = -2\). The slope formula between two points \((x_1, y_1)\) and \((x_2, y_2)\) is:

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

Substituting the values from the points \((2, x)\) and \((0, 8)\):

\[
-2 = \frac{x - 8}{2 - 0}
\]

Simplify:

\[
-2 = \frac{x - 8}{2}
\]

Multiply both sides by 2 to eliminate the denominator:

\[
-4 = x - 8
\]

Now, solve for \(x\):

\[
x = -4 + 8 = 4
\]

Thus, the missing coordinate is \(x = 4\), and the point is \((2, 4)\).

Would you like further details or have any questions?

Here are 5 related questions:
1. How is the slope formula derived?
2. What happens when the slope is zero?
3. How can we find the distance between two points given their coordinates?
4. How do you calculate the equation of a line given a point and the slope?
5. What if the slope was undefined?

**Tip:** Always double-check your substitution values when using formulas to avoid small errors.

Learn how to find the missing coordinate in a point using the slope formula. This problem uses algebraic and geometric concepts to solve for the unknown in the points (2,x) and (0,8) with a slope of -2. Suitable for students in Grades 8-10.

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