Final answer:
To find the equation of a line passing through two points, you can use the point-slope form of the equation: y - y₁ = m(x - x₁). Given the points (2,2) and (4,5), the equation of the line is 3x - 2y = 2.
Step-by-step explanation:
To find the equation of a line passing through two points, we can use the point-slope form of the equation: y - y₁ = m(x - x₁), where (x₁, y₁) and (x₂, y₂) are the coordinates of the two points, and m is the slope of the line.
Given the points (2,2) and (4,5), we can calculate the slope:
m = (y₂ - y₁) / (x₂ - x₁) = (5 - 2) / (4 - 2) = 3 / 2.
Substituting the coordinates of one of the points into the point-slope form, we can find the equation of the line: y - 2 = (3/2)(x - 2).
Rewriting the equation in the standard form, we get: 2y - 4 = 3x - 6. Simplifying, we have: 3x - 2y = 2.