Final answer:
The equation in standard form of the line y - 5 = -1/2 (x - 6) is x + 2y = 16.
Step-by-step explanation:
To find the equation of the line in standard form, we need to simplify the given equation. Let's distribute the -1/2 to both terms within the parentheses:
y - 5 = -1/2x + 3
Next, let's move the -5 to the other side by adding 5 to both sides:
y = -1/2x + 8
This is the simplified equation in slope-intercept form (y = mx + b), where m is the slope (-1/2) and b is the y-intercept (8). To convert it into standard form (Ax + By = C), we need to eliminate the fraction by multiplying both sides by 2:
2y = -x + 16
x + 2y = 16
So, the equation in standard form is x + 2y = 16.