Final answer:
To compute w1, w2, and b given intercepts in a linear equation, follow the steps of finding the slope and y-intercept. Use the formula w1 = (y2 - y1) / (x2 - x1) to calculate the slope. Substitute the values of w1, x1, and y1 into the equation y = mx + b to find the y-intercept (b). Use the equation w2 = y1 - w1 * x1 to calculate w2.
Step-by-step explanation:
To compute w1, w2, and b given intercepts, we need to understand the concept of intercepts in linear equations. In a linear equation in the form y = mx + b, where m is the slope and b is the y-intercept, the y-intercept represents the point where the line intersects the y-axis. It is the value of y when x is equal to 0. The slope represents the rate of change in y for every unit change in x.
To calculate the values of w1, w2, and b, we need to have two intercepts. Let's assume we have the intercepts (x1, y1) and (x2, y2).
1. To find the slope (w1), use the formula: w1 = (y2 - y1) / (x2 - x1).
2. To find the y-intercept (b), substitute the values of w1, x1, and y1 into the equation y = mx + b. Solve for b.
3. To find w2, use the equation: w2 = y1 - w1 * x1.
For example, if we have the intercepts (2, 4) and (5, 9), we can calculate:
w1 = (9 - 4) / (5 - 2) = 5 / 3
b = y1 - w1 * x1 = 4 - (5/3) * 2 = 4 - 10/3 = 2/3
w2 = y1 - w1 * x1 = 4 - (5/3) * 2 = 4 - 10/3 = 2/3