Final answer:
The equation of the line passing through (2,3) and (0,-1) is y = 2x - 1, found by calculating the slope and using the point-slope form to determine the y-intercept.
Step-by-step explanation:
To find the equation of the line passing through two points, (2,3) and (0,-1), we first need to calculate the slope (m) of the line. The slope is determined by the change in y over the change in x (rise over run), calculated as (y2 - y1)/(x2 - x1). Using the given points:
m = (3 - (-1))/(2 - 0) = 4/2 = 2
Now that we have the slope, we can use the point-slope form of the equation of a line to find the y-intercept (b). The point-slope form is given by (y - y1) = m(x - x1). Using one of the given points, (2,3):
3 - 2(2) = b
3 - 4 = b
-1 = b
With the slope and the y-intercept, we can write the equation in slope-intercept form (y = mx + b):
y = 2x - 1
Therefore, the correct answer is Option B.