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.