A line with a slope of 3/5 passes through points (1,-2) and (-3,K). What is the value of K?

To find the value of \( K \), we will use the slope formula. The slope \( m \) of a line that passes through two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is given by:

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

In this problem, the slope \( m \) is \( \frac{3}{5} \), and the points are \( (1, -2) \) and \( (-3, K) \). Substituting these values into the slope formula:

\[
\frac{3}{5} = \frac{K - (-2)}{-3 - 1}
\]

Simplifying the denominator on the right-hand side:

\[
\frac{3}{5} = \frac{K + 2}{-4}
\]

Now, multiply both sides by \( -4 \) to eliminate the denominator:

\[
\frac{3}{5} \times (-4) = K + 2
\]

Simplifying:

\[
-\frac{12}{5} = K + 2
\]

Now, subtract 2 from both sides to solve for \( K \). We need to rewrite 2 as a fraction with denominator 5:

\[
2 = \frac{10}{5}
\]

Thus:

\[
-\frac{12}{5} - \frac{10}{5} = K
\]

Simplifying:

\[
K = -\frac{22}{5}
\]

So, the value of \( K \) is \( -\frac{22}{5} \).

Would you like further details or clarifications?

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Here are 5 related questions:

1. How do you find the slope of a line if only the equation of the line is given?
2. What is the general form of a linear equation in slope-intercept form?
3. How can you find the y-intercept of a line if you know its slope and one point?
4. What happens if two lines have the same slope but different y-intercepts?
5. How do you calculate the distance between two points on a plane?

**Tip:** When calculating slope, always be careful with the signs in the numerator and denominator.

Learn how to find the value of K for a line with a slope of 3/5 that passes through the points (1, -2) and (-3, K). This problem involves key algebraic concepts and the slope formula. Suitable for students in Grades 8-10.

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