Final answer:
The equation in Standard Form of a line that passes through the point (10, -2) with a slope of -1/2 is x + 2y = 6.
Step-by-step explanation:
To write an equation in Standard Form of a line that passes through the point (10, -2) and has a slope of -1/2, you can start with the slope-intercept form of the line which is y = mx + b, where m is the slope and b is the y-intercept.
Knowing that the slope (m) is -1/2 and using the point (10, -2), we can substitute these values into the slope-intercept form to find b.
(-2) = (-1/2)(10) + b
b = -2 + 5
b = 3
Thus, the slope-intercept form of the line is y = (-1/2)x + 3.
To convert this to Standard Form (Ax + By = C), we multiply everything by 2 to eliminate the fraction:
2y = -x + 6
Then, we bring all terms to one side to get the final Standard Form of the equation:
x + 2y = 6