To find the equation of the line in slope-intercept form $y = mx + b$, we need to determine the slope $m$ and the y-intercept $b$.

Step 1: Calculate the slope $m$

The formula for the slope 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 $(5.0, 1300)$ and $(6.0, -850)$:

$m = \frac{-850 - 1300}{6.0 - 5.0} = \frac{-2150}{1} = -2150$

So, the slope $m = -2150$.

Step 2: Use the slope-intercept form

Now, we can use the slope-intercept form $y = mx + b$, where $m = -2150$, to find $b$.

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

Substitute one of the points, say $(5.0, 1300)$, into the equation $y = mx + b$:

$1300 = -2150(5.0) + b$

$1300 = -10750 + b$

$b = 1300 + 10750 = 12050$

Final Equation

The equation of the line is:

$y = -2150x + 12050$

Would you like any further details or clarification on this?

Here are 5 questions that expand on this concept:

1. How would the equation change if the points were reversed?
2. What does the slope of -2150 indicate about the direction of the line?
3. How would you interpret the y-intercept of 12050 in this context?
4. Can you find the x-intercept of this line?
5. How would the equation change if the slope were zero?

Tip: In slope-intercept form, the slope tells you the steepness and direction of the line, while the y-intercept indicates where the line crosses the y-axis.