Final answer:
Given the point (3, -2) and the slope m=2, neither of the provided options a) y = 2x - 2, b) y = 2x + 3, c) y = 2x - 3, nor d) y = 2x + 2 is correct. The valid slope-intercept form would be y = 2x - 8, calculated by substituting the given point into the equation and solving for the y-intercept.
Step-by-step explanation:
To write a linear equation in slope-intercept form given a point and the slope, we can use the formula y = mx + b, where m represents the slope and b represents the y-intercept. Given the point (3, -2) and the slope m = 2, we can substitute the slope and the point into the slope-intercept form to find the y-intercept.
The point (3, -2) tells us when x = 3, y = -2. Using the slope of 2, the equation becomes: -2 = 2(3) + b
Solve for b by subtracting 6 from both sides: b = -2 - 6 = -8
Therefore, the equation of the line is y = 2x - 8, which is not one of the options provided. However, the correct form of the equation is not listed in the options a) through d).