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Write the equation of the line in point-slope form.

The equation of a line in point-slope form is given by:

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

where \((x_1, y_1)\) is a point on the line and \(m\) is the slope of the line. From your image, the point \((2, 4)\) lies on the line.

To find the slope \(m\), we can use the information from the grid in the image. We need another point on the line to calculate the slope. It appears that the line crosses the y-axis at \(y = 0\) and the x-axis at \(x = 3\), giving us another point, \((3, 0)\).

Calculating the slope \(m\) using the points \((2, 4)\) and \((3, 0)\):

\[ m = \frac{0 - 4}{3 - 2} = \frac{-4}{1} = -4 \]

Now substituting \(m = -4\) and the point \((2, 4)\) into the point-slope equation:

\[ y - 4 = -4(x - 2) \]

Therefore, the equation of the line in point-slope form is:

\[ y - 4 = -4(x - 2) \]

Would you like further details or have any questions about this solution?

Here are some related topics:
1. How to convert this point-slope equation to the slope-intercept form \(y = mx + b\)?
2. How to derive the standard form of the equation of a line from point-slope form?
3. How to calculate the slope if given a graph without coordinates?
4. What is the significance of the slope and y-intercept in this context?
5. How to find the distance from a point to this line?

**Tip:** Always plot multiple points from the line equation to verify its correctness visually on a graph.

Learn how to find the equation of a line passing through the point (2, 4) using the point-slope form. This problem involves calculating the slope using two points on the line and applying the point-slope equation. Suitable for students in Grades 8-10.

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