Final answer:
The equation of the line passing through the points (2, 3) and (0, -1) is y = 2x - 1. After finding the slope using the rise over run method, the y-intercept was calculated using one of the points and the slope value.
Step-by-step explanation:
To find the equation of the line that passes through the points (2, 3) and (0, -1), we need to determine the slope (m) and y-intercept (b) of the line using the formula y = mx + b. The slope can be found by the formula (y2 - y1) / (x2 - x1), which represents rise over run. Using the given points:
- m = (3 - (-1)) / (2 - 0) = 4 / 2 = 2
With a slope of 2, we can plug one of the points into the slope-intercept form to solve for b:
- 3 = 2(2) + b
- 3 = 4 + b
- b = 3 - 4
- b = -1
Now, we have the slope m = 2 and y-intercept b = -1. Therefore, the equation of the line is y = 2x - 1, which corresponds to option B.