The pair of points (g,-1) and (2,5) lie on a line with a slope of 3/2. What is the value of g?
A. 4
B. -5
C. -2
D. 3
Let's use the slope-intercept form of a line, y = mx + b, where m is the slope and b is the y-intercept.
We are given that the slope is 3/2, so the equation of the line is y = (3/2)x + b.
We are also given that the points (g, -1) and (2, 5) lie on this line. Plugging in the coordinates of the point (g, -1) into the equation, we get:
-1 = (3/2)g + b
Similarly, plugging in the coordinates of the point (2, 5) into the equation, we get:
5 = (3/2)(2) + b
5 = 3 + b
Subtracting 3 from both sides of the second equation, we get:
2 = b
Now we can substitute this value of b into the first equation:
-1 = (3/2)g + 2
Subtracting 2 from both sides of this equation, we get:
-3 = (3/2)g
To solve for g, we can multiply both sides of this equation by 2/3:
(-3)(2/3) = (3/2)g(2/3)
-2 = g
Therefore, the value of g is -2. Answer choice C.