write an equation for the like passing through (8,10), (-4,-6)

To find the equation of the line passing through the points \((8, 10)\) and \((-4, -6)\), we follow these steps:

1. **Calculate the slope** (\(m\)) of the line using the formula:

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

Here, \((x_1, y_1) = (8, 10)\) and \((x_2, y_2) = (-4, -6)\).

\[ m = \frac{-6 - 10}{-4 - 8} = \frac{-16}{-12} = \frac{4}{3} \]

2. **Use the point-slope form** of the line equation:

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

We can use either point \((8, 10)\) or \((-4, -6)\). We'll use \((8, 10)\):

\[ y - 10 = \frac{4}{3}(x - 8) \]

3. **Simplify the equation** to the slope-intercept form (\(y = mx + b\)):

\[ y - 10 = \frac{4}{3}(x - 8) \]
\[ y - 10 = \frac{4}{3}x - \frac{32}{3} \]
\[ y = \frac{4}{3}x - \frac{32}{3} + 10 \]
\[ y = \frac{4}{3}x - \frac{32}{3} + \frac{30}{3} \]
\[ y = \frac{4}{3}x - \frac{2}{3} \]

So, the equation of the line passing through the points \((8, 10)\) and \((-4, -6)\) is:

\[ y = \frac{4}{3}x - \frac{2}{3} \]

Would you like more details or have any questions about this? Here are some related questions to expand your understanding:

1. How do you derive the slope formula for a line?
2. What is the point-slope form of a line, and why is it useful?
3. How can you convert from point-slope form to slope-intercept form?
4. What is the significance of the slope in the line equation?
5. How can you determine if two lines are parallel using their slopes?

**Tip:** Always double-check your calculations when determining the slope and rearranging equations to avoid mistakes.

write an equation for the line passing through (8,10), (-4,-6)

Learn how to find the equation of a line passing through points (8,10) and (-4,-6) using the slope formula and point-slope form. This step-by-step solution demonstrates how to calculate the slope and convert it into the slope-intercept form. Ideal for students in Grades 8-10.

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