Question

Find the equation of the linear relationship in slope-intercept form.

Given the points: (0, 100), (1.5, 96.5), (200, 300), (191.5, 286.5)
A) y = -0.5x + 100
B) y = -0.5x + 96.5
C) y = 0.5x + 100
D) y = 0.5x + 96.5

Answer 1

The equation of the linear relationship in slope-intercept form is y = -0.5x + 100.

Step-by-step explanation:

To find the equation of the linear relationship in slope-intercept form, we need to use the formula y = mx + b, where m is the slope and b is the y-intercept.

Given the points (0, 100), (1.5, 96.5), (200, 300), and (191.5, 286.5), we can calculate the slope using the formula
m = (y2 - y1) / (x2 - x1)

For the first two points, we get m = (96.5 - 100) / (1.5 - 0) = -0.5.
Now, substituting the slope and one of the points (0,100) into the formula, we can solve for b:
100 = -0.5(0) + b
100 = b

Therefore, the equation of the linear relationship in slope-intercept form is y = -0.5x + 100 (option A).