In the coordinate plane, line has a slope of 3 over 5 & passes through the point (-2,6)

To determine the equation of the line that has a slope of \(\frac{3}{5}\) and passes through the point \((-2, 6)\), we can use the point-slope form of a linear equation:

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

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

For this problem, the slope \(m = \frac{3}{5}\) and the point is \((-2, 6)\). Plugging in these values:

\[
y - 6 = \frac{3}{5}(x - (-2))
\]

Simplify the expression inside the parentheses:

\[
y - 6 = \frac{3}{5}(x + 2)
\]

Next, distribute \(\frac{3}{5}\):

\[
y - 6 = \frac{3}{5}x + \frac{3}{5} \times 2
\]

\[
y - 6 = \frac{3}{5}x + \frac{6}{5}
\]

To solve for \(y\), add 6 to both sides:

\[
y = \frac{3}{5}x + \frac{6}{5} + 6
\]

To combine \(\frac{6}{5}\) and 6, express 6 as a fraction with a denominator of 5:

\[
6 = \frac{30}{5}
\]

\[
y = \frac{3}{5}x + \frac{6}{5} + \frac{30}{5}
\]

\[
y = \frac{3}{5}x + \frac{36}{5}
\]

Thus, the equation of the line is:

\[
y = \frac{3}{5}x + \frac{36}{5}
\]

### Do you want more details or have any questions?

Here are some related questions for deeper exploration:
1. How would you write the equation of a line in standard form from this slope-intercept form?
2. What is the y-intercept of this line, and how can you determine it from the equation?
3. How can you verify if a given point lies on this line?
4. What would the equation be if the slope were negative instead, say \(-\frac{3}{5}\)?
5. How can you find the x-intercept of this line?

**Tip:** Point-slope form is a very handy tool when you have a point and a slope, as it allows for quick conversion to slope-intercept form!

Learn how to find the equation of a line with a slope of 3/5 passing through the point (-2, 6) using the point-slope form. This problem covers key algebra concepts and is suitable for students in Grades 8-10.

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