To find the equation of the line that passes through the points $(46, 338)$ and $(64, 392)$, we will first find the slope $m$, and then use the point-slope form to determine the equation in slope-intercept form.

Step 1: Find the slope $m$

The formula for the slope between two points $(x_1, y_1)$ and $(x_2, y_2)$ is given by:

$m = \frac{y_2 - y_1}{x_2 - x_1}$

Substitute the given points $(46, 338)$ and $(64, 392)$:

$m = \frac{392 - 338}{64 - 46} = \frac{54}{18} = 3$

So, the slope $m = 3$.

Step 2: Use the point-slope form of the equation

The point-slope form of the equation of a line is:

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

Using the point $(46, 338)$ and the slope $m = 3$, we substitute into the equation:

$y - 338 = 3(x - 46)$

Step 3: Convert to slope-intercept form

Now, simplify the equation to get it in slope-intercept form $y = mx + b$:

$y - 338 = 3(x - 46)$

Distribute the 3:

$y - 338 = 3x - 138$

Now, add 338 to both sides:

$y = 3x - 138 + 338$

$y = 3x + 200$

Final Answer:

The equation of the line in slope-intercept form is:

$y = 3x + 200$

---

Would you like any further details or have any questions on the solution? Here are some related questions:

1. How do you find the slope if you only have one point and the equation of the line?
2. What is the relationship between slope and the steepness of a line?
3. How can you determine if two lines are parallel or perpendicular based on their slopes?
4. How would the equation change if we were given a different pair of points?
5. How do you convert from standard form to slope-intercept form?

Tip: Always double-check the calculation of the slope before proceeding to ensure the rest of your work follows correctly!