Question 7003
The assumption is that he will scale linearly.
Let y be the new score and x be the old score.
So,
{{{y = mx + b}}}
We can calculate the slope between the two points (40, 60) and (80,90) by
{{{(90-60)/(80-40)=30/40=3/4}}}
So,
{{{y=(3/4)x + b}}}
The value of b will be determined substituting one set of values for x and y.
{{{90 = (3/4)80 + b=60+b}}}
{{{90-60=30=b}}}
The equation of the line which indicates the scaling is
{{{y = (3/4)x + 30}}}
Checking:
y=3/4 x 40 + 30 = 30 + 30 = 60 [putting in 40 for x shows y is 60]
y=3/4 x 80 + 30 = 60+30 = 90 [80 converts to 90]

An x=45 would produce what y? [You do it. Hint: I got 63 3/4]
A y=84 would produce what x [You do it]