Final answer:
The general linear equation for the line through the points (1,1) and (2,3) is y = 2x - 1.
Step-by-step explanation:
The general linear equation for a line can be written in the form y = mx + b, where m represents the slope of the line and b represents the y-intercept.
To find the slope, we use the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of the given points.
Using the points (1,1) and (2,3), we have m = (3 - 1) / (2 - 1) = 2.
Now that we know the slope, we can plug it into the equation to get y = 2x + b. To find the y-intercept, we can substitute the coordinates of one of the points into the equation. Using (1,1), we have 1 = 2(1) + b, which gives us b = -1.
Therefore, the general linear equation for the line through the two points (1,1) and (2,3) is y = 2x - 1.