How to solve - A line passes through point (8,7) with a slope of K . The Y-intercept of this line is given by the expression

To find the y-intercept of a line that passes through a point \((8, 7)\) with a slope \(K\), you can use the point-slope form of a linear equation.

The 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.

Given:
- The point \((x_1, y_1) = (8, 7)\)
- The slope \(m = K\)

Substitute these values into the equation:

\[
y - 7 = K(x - 8)
\]

Now, convert this into slope-intercept form \(y = mx + b\), where \(b\) is the y-intercept:

1. Expand and simplify the equation:
   \[
   y - 7 = K(x - 8)
   \]
   \[
   y - 7 = Kx - 8K
   \]

2. Solve for \(y\):
   \[
   y = Kx - 8K + 7
   \]

In this equation, the y-intercept \(b\) is the constant term when \(x = 0\). So, the y-intercept is:

\[
b = -8K + 7
\]

### Final Answer:
The y-intercept of the line is given by the expression \(b = -8K + 7\).

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Do you want more details or have any questions? Here are 5 related questions for further exploration:

1. What is the general formula for finding the y-intercept of a line given a point and a slope?
2. How do you find the slope of a line if you're given two points instead of one point and the slope?
3. How can you graph a line given a point and a slope?
4. What happens to the y-intercept if the slope \(K\) is zero?
5. How can you find the equation of a line that is perpendicular to the given line?

**Tip:** Always ensure your equation is in the correct form (such as slope-intercept form) before identifying the y-intercept.

Learn how to find the y-intercept of a line passing through the point (8, 7) with a given slope K using the point-slope form and slope-intercept form. Detailed step-by-step solution provided.

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