Final answer:
The standard form of the equation of the line passing through (-3, 6) and (3, 10) is (2/3)x - y = -4.
Step-by-step explanation:
To find the standard form of the equation of the line passing through the points (-3, 6) and (3, 10), we can use the point-slope form of a linear equation. The formula for the point-slope form is y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope.
First, let's find the slope using the formula: m = (y2 - y1) / (x2 - x1). Plugging in the values, we get m = (10 - 6) / (3 - (-3)) = 4 / 6 = 2/3.
Next, we can choose either (-3, 6) or (3, 10) as our point (x1, y1) and substitute the values into the point-slope form. Let's choose (-3, 6): y - 6 = (2/3)(x - (-3)). Simplifying, we get y - 6 = (2/3)x + 2. Rearranging the equation to match the standard form Ax + By = C, we get (2/3)x - y = -4.