The graph shows the number of gallons in a waiting pool that is being drained using the points (1,160) and (3,80) as (
x₁, y₁) and (x₂, y₂) respectively.
To find the equation of the line passing through these points, we can use the slope-intercept form of a linear equation:
y = mx + b
where m represents the slope and b represents the y-intercept.
The slope of a line passing through two points (x₁, y₁) and (x₂, y₂) can be calculated using the formula:
m = (y₂ - y₁) / (x₂ - x₁)
Plugging in the given values, we have:
m = (80 - 160) / (3 - 1)
= -80 / 2
= -40
Now, we can substitute the slope (m) into the slope-intercept form and solve for the y-intercept (b) using one of the given points.
Using the point (1, 160):
160 = -40(1) + b
160 = -40 + b
b = 200
Therefore, the equation of the line is y = -40x + 200.