The given equation of line $f$ is in point-slope form:

$y - 7 = \frac{3}{10}(x - 4)$

Step 1: Identify the slope of line $f$

The slope $m$ of the line $f$ is the coefficient of $(x - 4)$, which is $\frac{3}{10}$.

Since line $g$ is parallel to line $f$, it will have the same slope.

Thus, the slope of line $g$ is also $\frac{3}{10}$.

Step 2: Use the point-slope form for line $g$

Line $g$ passes through the point $(10, 4)$, so we can use the point-slope formula to write the equation of line $g$:

$y - y_1 = m(x - x_1)$

Where:

• $m = \frac{3}{10}$ (slope),
• $(x_1, y_1) = (10, 4)$ (a point on the line).

Substitute these values into the equation:

$y - 4 = \frac{3}{10}(x - 10)$

Step 3: Simplify the equation

Now, simplify the equation to put it in slope-intercept form (if desired):

$y - 4 = \frac{3}{10}(x - 10)$

Distribute the $\frac{3}{10}$:

$y - 4 = \frac{3}{10}x - 3$

Now, add 4 to both sides:

$y = \frac{3}{10}x + 1$

Final Answer:

The equation of line $g$ is:

$y = \frac{3}{10}x + 1$

Would you like more details or have any questions about this process? Here are a few related questions:

1. What are the different forms of a linear equation, and how do they relate to each other?
2. How do you convert between point-slope form and slope-intercept form?
3. Can two lines be parallel with different y-intercepts?
4. How do you find the equation of a line when you're given two points on the line?
5. What is the significance of the slope in the context of real-world problems?

Tip: When working with parallel lines, remember that the slopes are always equal, but the y-intercepts might differ!