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The linear equation is:

# AIDS cases diagnosed $=-3448225+1750$(year).

To find the value of $\hat{y}$:

$x=1985$

Therefore, the linear equation will be written as shown below:

# AIDS cases diagnosed$=-3448225+1750$(year)

# AIDS cases diagnosed$=-3448225+1750\left(1985\right)$

$=2552$

The linear equation is:
# AIDS cases diagnosed$=-3448225+1750$(year).

To find the value of $\hat{y}$:

$x=1990$

Therefore, the linear equation will be written as shown below:

# AIDS cases diagnosedlocalid="1649165820824" $=-3448225+1750$(year)

# AIDS cases diagnosedlocalid="1649165489151" $=-3448225+1750\left(1990\right)$

$=34275$

The linear equation is :

# AIDS cases diagnosed$=-3448225+1750$(year).

To find the value of $\hat{y}$:

$x=1970$

Therefore, the linear equation will be written as shown below:

# AIDS cases diagnosedlocalid="1649165349688" $=-3448225+1750$(year)

# AIDS cases diagnosedlocalid="1649165322240" $=-3448225+1750\left(1970\right)$

$=-725$

It is known that the range of variable "year" is $1981-2002$. The year $1970$is not in the range.