Find the equation of the line using the point slope formula. (1,2) with a slope of -4/5

To find the equation of the line using the point-slope formula, you can use the following formula:

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

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

Given:
- Point: \((1, 2)\)
- Slope: \(m = -4/5\)

Substitute these values into the point-slope formula:

\[
y - 2 = \frac{-4}{5}(x - 1)
\]

To write this equation in slope-intercept form (optional), you can simplify:

\[
y - 2 = \frac{-4}{5}x + \frac{4}{5}
\]

\[
y = \frac{-4}{5}x + \frac{4}{5} + 2
\]

\[
y = \frac{-4}{5}x + \frac{4}{5} + \frac{10}{5}
\]

\[
y = \frac{-4}{5}x + \frac{14}{5}
\]

So, the equation of the line is:

\[
y = \frac{-4}{5}x + \frac{14}{5}
\]

Would you like more details or have any questions?

Here are 5 related questions:
1. How can you convert the point-slope form to standard form?
2. What would the equation look like if the slope were positive?
3. How do you find the x-intercept of this line?
4. What is the significance of the y-intercept in the context of this equation?
5. How would the equation change if the point were \((2, 3)\) instead?

**Tip:** Always verify your equation by plugging the point back into it to ensure it satisfies the equation.

Learn how to find the equation of a line using the point-slope formula with a given point (1, 2) and slope -4/5. This problem covers key concepts in linear equations and slope calculations. Suitable for students in Grades 7-9.

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