SAT Desmos Regression: Build a Linear Model from a Table

Add a table and enter the four pairs below in columns x₁ and y₁.

The labels are the table’s variables, not ordinary x and y. Desmos’s table names may increment if you already have another table; use the names actually shown.

In a new expression line, type:

y_1 ~ m x_1 + b

The underscore creates the subscript, and the tilde requests a fit. This exact table gives m = 4 and b = 5. The fitted equation is y = 4x + 5. You can also use a regression template where available; typing the custom model makes the chosen form explicit.

Consecutive points differ by 1 in x and 4 in y, so the slope must be 4. Substitute (1,9): 9 = 4(1) + b, giving b = 5. Every point satisfies y = 4x + 5, so all residuals are zero for this deliberately exact example.

Define f(x) = 4x + 5 and enter f(6). The model predicts 29. Because x = 6 lies beyond the observed x-range from 1 to 4, this is extrapolation. The problem may ask for the model’s prediction, but an actual future measurement need not equal it. A fitted association alone does not establish causation.

For (1,7), (2,10), (3,13) and (4,16), the constant rate is 3 and the intercept is 4. Enter the table and fit the same linear model: y = 3x + 4. At x = 5 the predicted y-value is 19. If the data are visibly curved, investigate the requested model rather than choosing a line automatically.