#### Answer

The linear function in slope intercept form that models the total spending, $p\left( x \right)$, by Americans x years after $1950$ is $p\left( x \right)=-0.25x+22$.

#### Work Step by Step

From the provided information, the rate of change of decrease in the budget is provided as $0.25\%$. This represents the slope with a negative sign.
$m=-0.25$.
And the value of c is provided as $22\%$ because the Americans spent $22\%$ of their budget in $1950$ (which is the starting year that shows y the intercept).
Substitute the values $m=-0.25$ and $c=22$.
The obtained linear model is:
$p\left( x \right)=-0.25x+22$.
Hence, the linear function in slope-intercept form that models the total spending is $p\left( x \right)=-0.25x+22$.