Answer: To find the equation of the line passing through the points (-9, -2) and (7, 6) in standard form, we can follow these steps:
Step 1: Determine the slope of the line using the formula:
slope = (y2 - y1) / (x2 - x1)
Plugging in the coordinates of the two points:
slope = (6 - (-2)) / (7 - (-9))
= 8 / 16
= 1/2
Step 2: Use the point-slope form of a line to write the equation. We'll use the first given point (-9, -2):
y - y1 = m(x - x1)
y - (-2) = 1/2(x - (-9))
y + 2 = 1/2(x + 9)
2y + 4 = x + 9
x - 2y = -5
Step 3: Rewrite the equation in standard form, which is in the form Ax + By = C. Let's multiply the entire equation by 2 to eliminate the fraction:
2(x - 2y) = 2(-5)
2x - 4y = -10
So, the equation of the line passing through the points (-9, -2) and (7, 6) in standard form is 2x - 4y = -10.
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Explanation: