In 1990, a company had a profit of $1.3 million. In 1992, the company had a profit of $1.2 million. Write a linear equation giving the profit P, in millions of dollars, in terms of the year, t. Let t=0 represent 1990.
P = to + 0.5*t
Check it carefully. Substitute 1.2 million for to, then t = 2 years.
To write a linear equation giving the profit P in terms of the year t, we need to find the equation of a line that passes through two points: (1990, 1.3) and (1992, 1.2).
We can use the slope-intercept form of a linear equation, which is given by:
y = mx + b
where m is the slope of the line and b is the y-intercept.
First, let's find the slope (m) using the formula:
m = (y2 - y1) / (x2 - x1)
where (x1, y1) = (1990, 1.3) and (x2, y2) = (1992, 1.2).
Substituting the values into the formula, we have:
m = (1.2 - 1.3) / (1992 - 1990)
= -0.1 / 2
= -0.05
Now, we have the slope (m). Next, let's find the y-intercept (b) by substituting one of the points and the slope into the equation:
1.3 = (-0.05)(1990) + b
Simplifying the equation, we have:
1.3 = -99.5 + b
Now, we can solve for b by isolating it:
b = 1.3 + 99.5
= 100.8
Therefore, the equation of the line is:
P = -0.05t + 100.8
where P represents the profit in millions of dollars and t represents the year, with t=0 representing 1990.