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!