Final answer:
The equation of the line that passes through the points (-2, 2) and (-5, -4) is y = 2x + 6.
Step-by-step explanation:
To find the equation of the line that passes through the points (-2, 2) and (-5, -4), we can use the slope-intercept form of a linear equation, y = mx + b. The slope (m) can be determined by calculating the difference in y-coordinates divided by the difference in x-coordinates, which is (y2 - y1) / (x2 - x1). Plugging in the values, we get (2 - (-4)) / (-2 - (-5)) = 6 / 3 = 2. Therefore, the slope of the line is 2.
Now, we can substitute the slope and one of the points into the equation y = mx + b to find the y-intercept (b). Using the point (-2, 2), we have 2 = 2(-2) + b. Solving for b, we get b = 2 + 4 = 6.