Let's work through the problem based on the details visible in the image.

Part (a)

You're asked to create a linear equation in slope-intercept form $y = mx + b$ where:

• $y$ represents the number of immigrants.
• $t$ is the number of years after 1900.

We have two points to determine the slope $m$:

1. In 1950 ($t = 50$), the number of immigrants was 246,046.
2. In 2003 ($t = 103$), the number of immigrants was 1,100,712.

We can use the slope formula: $m = \frac{y_2 - y_1}{x_2 - x_1}$ Substitute the values: $m = \frac{1,100,712 - 246,046}{103 - 50} = \frac{854,666}{53} \approx 16,125.78$

Now, using the point-slope form $y - y_1 = m(t - t_1)$, we can plug in one of the points, say $(50, 246,046)$, to find the equation. This gives: $y - 246,046 = 16,125.78 (t - 50)$ Simplifying: $y = 16,125.78t - 806,289.94 + 246,046$ $y \approx 16,125.78t - 560,243.94$

So, the equation of the line is approximately: $y = 16,125.78t - 560,243.94$

This is the linear equation in slope-intercept form that models the number of immigrants admitted based on the number of years after 1900.

Would you like further assistance with part (b) or (c) of the problem?

Here are five related questions you could explore:

1. How can you use this equation to predict future immigration trends?
2. What assumptions does this linear model make about immigration?
3. What would happen to the model if immigration changes accelerated significantly after 2003?
4. Can you find the x-intercept, and what does it represent in the context of this problem?
5. How could you modify this model to account for non-linear growth?

Tip: To ensure accuracy when solving for slope or intercepts, keep track of decimal places and rounding rules.