Write an equation of the line passing through 3 5 and 2 6 Gi

Write an equation of the line passing through (-3, 5) and (2, 6). Give the answer in standard form. The equation of the line in standard form is .

Solution

The slope-intercept form of the equation of a line is y = mx +c where m is the slope and c is the y -intercept. Here, the slope is (y₂ - y₁)/ (x₂ - x₁) = (6 - 5)/[ 2 - (-3)] = 1/5. Then, the equation of the line changes to y = x/5 + c.Since the required line passes through the point (2 , 6), on substituting x = 2 and y = 6 in the line\'s equation,.we have 6 = 2/5 + c or, c = 6 -2/5 = (30-2)/5 = 28/5. Then on substituting c = 28/5 in the equation of the line, we have y = x/5 + 28/5 or, on multiplying both the sides by 5, 5y = x + 28 or, x - 5y + 28 = 0. We can verify the result by substituting x = -3 and y = 5 in this equation.Thus, the equation of the required line in standard form is x - 5y + 28 = 0