Final answer:
To calculate the y-intercept of a line given two points, use the formula y = mx + b, where m is the slope and b is the y-intercept. Find the slope using the formula (Y₂ - Y₁) / (X₂ - X₁), then substitute the slope and the coordinates of one point into the y = mx + b formula and solve for b.
Step-by-step explanation:
In order to calculate the y-intercept of a line given two points, you need to use the formula y = mx + b, where m is the slope and b is the y-intercept. First, calculate the slope of the line using the formula m = (Y₂ - Y₁) / (X₂ - X₁), where Y₂ and Y₁ are the y-values of the two points and X₂ and X₁ are the x-values. Then, substitute the slope and the coordinates of one of the points into the formula y = mx + b and solve for b to find the y-intercept.
For example, if you have the points (2, 5) and (4, 9), you would calculate the slope as (9 - 5) / (4 - 2) = 2. Then, substituting the slope (2) and the coordinates of one of the points (2, 5) into the formula y = mx + b, you would have 5 = 2(2) + b. Solve for b by isolating the variable: b = 5 - 4 = 1. Therefore, the y-intercept is 1.