Step 1: Identify the point and the line. The point is (3, 4) and the line is given by the equation 2x + 3y - 6 = 0.
Step 2: Substitute the x and y values of the point into the line equation. This means we will calculate 2(3) + 3(4) - 6.
Step 3: Calculate the result of the substitution. First, calculate 2(3) = 6, then 3(4) = 12. Now add these results: 6 + 12 = 18. Finally, subtract 6: 18 - 6 = 12.
Step 4: Take the absolute value of the result from Step 3. The absolute value of 12 is |12| = 12.
Step 5: Calculate the denominator, which is the square root of the sum of the squares of the coefficients of x and y in the line equation. The coefficients are 2 and 3, so calculate √(2² + 3²) = √(4 + 9) = √13.
Step 6: Divide the absolute value from Step 4 by the result from Step 5. This gives us Distance = 12 / √13.
