Final answer:
The equation of the line passing through the points (2/5, 19/20) and (1/3, 11/12) in slope-intercept form is y = -1/28x + 67/70.
Step-by-step explanation:
To find the equation of the line passing through the points (2/5, 19/20) and (1/3, 11/12) in slope-intercept form, we need to find the slope and the y-intercept.
Step 1:
Find the slope (m) using the formula:
m = (y2 - y1) / (x2 - x1)
Plugging in the coordinates of the points, we get:
m = (11/12 - 19/20) / (1/3 - 2/5)
m = (-1/60) / (-7/15)
m = - (1/60) * (15/7)
m = -1/28
Step 2:
Use the slope-intercept form: y = mx + b
y = -1/28x + b
Step 3:
Substitute the coordinates of one of the points to find the value of b:
19/20 = -1/28(2/5) + b
Simplifying the equation gives:
19/20 = -1/70 + b
b = 19/20 + 1/70
b = 67/70
Step 4:
Plug the value of b back into the equation:
Therefore, the equation of the line is y = -1/28x + 67/70.