Final answer:
To determine the standard form equation of a line passing through the points (7, 5) and (11, -7), you calculate the slope, use it to find the y-intercept, and then rearrange the equation. The correct standard form equation is 3x + y = 26.
Step-by-step explanation:
To find the equation of the line in standard form that passes through the points (7, 5) and (11, -7), first, we need to calculate the slope (m) of the line using the slope formula:
m = (y2 - y1) / (x2 - x1)
Substituting the given points into the formula, we get:
m = (-7 - 5) / (11 - 7) = -12 / 4 = -3
With the slope known, we choose one of the points to find the y-intercept (b) using the formula for a line, y = mx + b. Let's use the point (7, 5):
5 = (-3)(7) + b
b = 5 + 21 = 26
The equation of the line in slope-intercept form is:
y = -3x + 26
To convert this to standard form, where Ax + By = C, we rearrange the terms:
3x + y = 26
This matches option D from the given choices. Hence, the correct equation in standard form of the line passing through the points (7, 5) and (11, -7) is 3x + y = 26.