A linear relationship has a slope of negative 2 and passes through the point open parentheses 8 comma negative 10 close parentheses
Write an equation to represent this linear relationship.

To find the equation of a line with a given slope and a point it passes through, we use the **point-slope form** of a linear equation:

\[
y - y_1 = m(x - x_1)
\]

where:
- \( m \) is the slope,
- \( (x_1, y_1) \) is a point on the line.

Given:
- Slope \( m = -2 \),
- Point \( (x_1, y_1) = (8, -10) \).

Substitute these values into the point-slope form:

\[
y - (-10) = -2(x - 8)
\]

Simplify:

\[
y + 10 = -2x + 16
\]

Now, isolate \( y \) to write the equation in slope-intercept form \( y = mx + b \):

\[
y = -2x + 6
\]

**Final equation:** 

\[
y = -2x + 6
\]

Would you like further details or have any questions?

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Here are 5 related questions:
1. How would the equation change if the slope was positive?
2. What is the y-intercept of the equation \( y = -2x + 6 \)?
3. How can we find another point on the line using the equation?
4. How do we convert the equation to standard form?
5. What does the slope of \(-2\) tell us about the line's direction?

**Tip:** To find the y-intercept, set \( x = 0 \) in the linear equation.

A linear relationship has a slope of -2 and passes through the point (8, -10). Write an equation to represent this linear relationship.

Learn to write a linear equation with a slope of -2 that passes through the point (8, -10). This problem covers algebraic concepts including the point-slope form and converting to slope-intercept form. Suitable for students in Grades 8-10.

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