The equation that contains the points (-2, -2) and (4, 10) is y - 6 = 2(x - 2).
Here's how we can find the equation:
Calculate the slope: The slope (m) of the line passing through the two points can be calculated using the formula:
m = (y2 - y1) / (x2 - x1)
where (x1, y1) = (-2, -2) and (x2, y2) = (4, 10).
Substituting the values, we get:
m = (10 - (-2)) / (4 - (-2))
m = 12 / 6
m = 2
Substitute the slope and a point into the point-slope form: The point-slope form of the equation of a line is:
y - y1 = m(x - x1)
where m is the slope and (x1, y1) is a point on the line.
We can use either of the given points, so let's use (-2, -2):
y - (-2) = 2(x - (-2))
y + 2 = 2(x + 2)
y + 2 = 2x + 4
y = 2x + 2
Simplify the equation: Finally, we can simplify the equation by rearranging the terms:
y = 2x + 2 - 2
y = 2x + 0
y = 2x
However, none of the answer choices match the equation we derived. This might be because the question contains an error.
The points (-2, -2) and (4, 10) do not lie on a straight line with a slope of 2. Therefore, the equation y - 6 = 2(x - 2) is not the correct answer to this question.