Final answer:
To find the equation of a line given two points, we need to find the slope using the formula m = (y2 - y1) / (x2 - x1), then substitute one of the points into the slope-intercept form of the equation y = mx + b to find the y-intercept. Therefore, the equation of the line is y = (-3/2)x - 1 1/2.
Step-by-step explanation:
To find the equation of a line given two points, we need to use the slope-intercept form of the equation, y = mx + b, where m is the slope of the line and b is the y-intercept. First, we need to find the slope of the line using the formula m = (y2 - y1) / (x2 - x1). Let's use the points (-4, 2 1/2) and (8,-2) to find the slope:
m = (-2 - 2 1/2) / (8 - (-4)) = (-2 - 5/2) / (8 + 4) = -9/6 = -3/2
Next, we can choose either of the given points to substitute into the equation y = mx + b to find b. Let's use the point (-4, 2 1/2):
2 1/2 = (-3/2)(-4) + b
2 1/2 = 6 + b
b = 2 1/2 - 6
b = -1 1/2
Therefore, the equation of the line is y = (-3/2)x - 1 1/2.