Question

Write the point-slope form of the equation of the line that passes through the two points. $$ (1,3),(2,5) $$

Short answer

The point-slope form of the equation of the line that passes through the points (1,3) and (2,5) is \(y - 3 = 2(x - 1)\).

Step-by-step solution

Calculate the slope of the line

To calculate the slope of the line, use the formula \(m = (y2 - y1) / (x2 - x1)\), substituting the given points (1, 3) for \((x1, y1)\) and (2, 5) for \((x2, y2)\). Therefore, \(m = (5 - 3) / (2 - 1) = 2 / 1 = 2\).

Write the point-slope form of the equation

The point-slope form of the equation of a line is \(y - y1 = m(x - x1)\). So, using the calculated slope (m = 2) and one of the given points (for instance, (1, 3)), the equation is \(y - 3 = 2(x - 1)\).