Bunuel
What is the equation of the line that passes through the points (−4, 3) and (6, −2) ?
A. y = −1/2*x + 1
B. y = −1/2*x + 2
C. y = 1/2*x + 5
D. y = 1/2*x + 7
E. y = 1/2*x + 8
First, let's determine the slope, using the two ordered pairs:
Slope = (y2 - y1)/(x2 - x1) = (-2 - 3)/(6 - (-4)) = -5/10 = -1/2
Next we can determine the y-intercept. We could use either ordered pair to get the x and y values to substitute into the slope-intercept form of the line, but we choose (6, -2).
-2 = (6)(-1/2) + b
-2 = -3 + b
1 = b
Thus, the equation is y = −1/2*x + 1.
Alternate Solution:
Letting the equation of the line be y = mx + n, we note that both of these points must satisfy this equation since they are on this line.
From the first point, substituting x = -4 and y = 3, we obtain the equation 3 = -4m + n.
From the second point, substituting x = 6 and y = -2, we obtain the equation -2 = 6m + n.
Subtracting the second equation from the first, we find that 5 = -10m; therefore m = -1/2.
Multiplying the first equation by 3/2 and adding to the second equation, we find 9/2 - 2 = 3n/2 + n. Simplifying, we get 5/2 = 5n/2; which implies n = 1.
Thus, the equation of the line is y =-1/2*x + 1.
Answer: A