Final answer:
The equation in slope-intercept form for the line that passes through the point (-2, 2) and is parallel to the line y = (3/2)x - 3 is y = (3/2)x + 5.
Step-by-step explanation:
To find the equation of a line that is parallel to the line y = (3/2)x - 3 and passes through the point (-2, 2), we need to use the slope-intercept form of the equation, which is y = mx + b. The given line has a slope of 3/2, so the parallel line will also have the same slope. We can use this slope and the given point to find the y-intercept (b) of the parallel line.
Using the point-slope form of the equation, which is y - y1 = m(x - x1), we can substitute the slope and the coordinates of the given point into the equation and solve for y to get the equation in slope-intercept form.
Substituting the values, we get y - 2 = (3/2)(x - (-2)). Simplifying the equation, we have y - 2 = (3/2)(x + 2). Multiplying through by 2, we get 2(y - 2) = 3(x + 2). Expanding and rearranging the terms, we get 2y - 4 = 3x + 6. Finally, adding 4 to both sides, we get 2y = 3x + 10. Dividing both sides by 2, the equation is y = (3/2)x + 5.