Final answer:
The equation of the line with slope -3/2 that passes through the point (-1,2) in slope-intercept form is y = -3/2x + 5/2.
Step-by-step explanation:
To find the equation of the line in slope-intercept form (y = mx + b), where 'm' is the slope and 'b' is the y-intercept, we use the given slope and the point through which the line passes. In this case, the slope is given as -3/2, and the line passes through the point (-1, 2).
First, we plug the slope (m = -3/2) into the slope-intercept form:
y = (-3/2)x + b
Next, we use the coordinates of the given point (-1, 2) to find the y-intercept (b). We plug x = -1 and y = 2 into the equation:
2 = (-3/2)(-1) + b
Solving for 'b', we get:
2 = 3/2 + b
b = 2 - 3/2
b = 4/2 - 3/2
b = 1/2
Now that we have both the slope and the y-intercept, we can write the final equation:
y = (-3/2)x + 1/2
Matching this with the given options, the correct equation is:
b) y = -3/2x + 5/2