Final answer:
To write the equation of a line with a slope of -1/2 passing through (-6,-3) in standard form, use the point-slope equation and then rearrange the terms to get x + 2y = -9, which is in the standard form Ax + By = C.
Step-by-step explanation:
To write an equation in standard form given a line that passes through (-6,-3), with a slope (m) of -1/2, you must use the point-slope form of the equation of a line, which is y - y1 = m(x - x1), where (x1, y1) are the coordinates of the given point and m is the slope. Plugging in the given point and slope, we get y - (-3) = (-1/2)(x - (-6)), which simplifies to y + 3 = (-1/2)(x + 6). To convert this to standard form, multiply out the right side and then get all terms involving x and y on the left side of the equation, bringing constants to the right side. The equation becomes y + 1/2x = -3 - 1/2(6), which further simplifies to 2y + x = -6 - 3 or x + 2y = -9, which is the standard form Ax + By = C.
The slope (m) and the y-intercept (b) are used to describe the shape and position of a line on a graph. The slope is the ratio of the rise over run between any two points on the line, and the y-intercept is the point where the line crosses the y-axis. The standard form equation Ax + By = C can be manipulated into slope-intercept form y = mx + b to easily identify these values.