Answer:
To find the equation of a line that passes through two points, (-2, 7) and (6, -9), you can use the point-slope form of the equation:
\[y - y_1 = m(x - x_1)\]
Where (x₁, y₁) is one of the points on the line, and m is the slope of the line.
First, let's find the slope (m) using the two given points:
m = \((y_2 - y_1) / (x_2 - x_1)\)
Using the points (-2, 7) and (6, -9):
m = \((-9 - 7) / (6 - (-2))\)
m = \((-16) / (6 + 2)\)
m = \(-16 / 8\)
m = \(-2\)
Now that we have the slope (m), we can use one of the points, say (-2, 7), in the point-slope form:
\(y - 7 = -2(x - (-2))\)
Now simplify:
\(y - 7 = -2(x + 2)\)
Distribute the -2 on the right side:
\(y - 7 = -2x - 4\)
Now, isolate y by adding 7 to both sides:
\(y = -2x - 4 + 7\)
\(y = -2x + 3\)
So, the equation of the line that passes through the points (-2, 7) and (6, -9) is:
\[y = -2x + 3\]
The correct answer is B) \(y = -2x + 3\).
Explanation: