Answer:
2. y = -3x + 32
Explanation:
To find the equation of a line passing through two points, you can use the point-slope form of a line. The slope m of the line can be calculated using the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of the two points. In this case, the slope is m = (-4 - 2) / (12 - 10) = -6 / 2 = -3.
Once you have the slope, you can use one of the points and the point-slope form y - y1 = m(x - x1) to find the equation of the line. Substituting the values for m, x1, and y1 gives us y - 2 = -3(x - 10). To simplify the equation y - 2 = -3(x - 10), you can start by distributing the -3 on the right side of the equation: y - 2 = -3x + 30. Then, you can add 2 to both sides of the equation to isolate y on the left side: y - 2 + 2 = -3x + 30 + 2, which simplifies to y = -3x + 32.
Therefore, the correct answer is Option 2. y = -3x + 32