Final answer:
To find the equation of a line passing through two points, use the slope-intercept form y = mx + b. Calculate the slope using (Y₂ - Y₁) / (X₂ - X₁), and substitute one of the points and the slope into the equation to solve for the y-intercept.
Step-by-step explanation:
To find the equation of a line passing through two points, let's use the slope-intercept form, y = mx + b. The slope (m) is given by (Y₂ - Y₁) / (X₂ - X₁), where (X₁, Y₁) and (X₂, Y₂) are the coordinates of the two points. Once you have the slope, you can substitute one of the points and the slope into the equation to solve for the y-intercept (b).
For example, if the two points are (1, 2) and (3, 4), the slope is (4 - 2) / (3 - 1) = 1. The equation becomes y = 1x + b. To find b, we can substitute either point into the equation. Let's use (1, 2): 2 = 1(1) + b. Solving for b, we get b = 1.
Therefore, the equation of the line passing through the points (1, 2) and (3, 4) is y = x + 1.