To write the equation of the line in slope-intercept form $y = mx + b$, passing through the points $(5, 4)$ and $(-5, -10)$, we need to follow these steps:

Step 1: Find the slope $m$

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

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

Substitute the given points $(5, 4)$ and $(-5, -10)$:

$m = \frac{-10 - 4}{-5 - 5} = \frac{-14}{-10} = 1.4$

Step 2: Use the slope-intercept form

Now that we have the slope $m = 1.4$, substitute this into the equation $y = mx + b$.

Step 3: Solve for the y-intercept $b$

Use one of the given points, say $(5, 4)$, to solve for $b$:

$4 = 1.4(5) + b$ $4 = 7 + b$ $b = 4 - 7 = -3$

Final equation

Thus, the equation of the line is:

$y = 1.4x - 3$

Let me know if you need further details or explanations! Here are 5 related questions you might want to explore:

1. How would the equation change if the slope was negative?
2. What is the geometric interpretation of the y-intercept?
3. How can we rewrite the equation of the line in point-slope form?
4. How would you check if another point lies on the line?
5. What is the significance of parallel and perpendicular slopes?

Tip: When finding the equation of a line from two points, always calculate the slope first, as it defines the steepness and direction of the line.