Question

Find a linear function f(x) = ax+b for which f(2)=1 and f(-3) =11

Answer 1

so we have to compute f(x)=y=ax+b
see by the given data (2,1) and (-3,11) are the points on the line y=ax+b

Answer 2

so compute the slope first which is (y2-y1)/(x2-x1)=(11-2)/(-3-2)=10/(-5)=-2
so a=slope=-2

Answer 3

now the equation takes the form y=-2x+b put x=2 and y=1 (since (2,1) satisfies the line)
and you have 1=-2.2+b implies b=1+4=5

Answer 4

so the final equation is y=f(x)=-2x+5

Answer 5

@chillhill

Answer 6

Thank you so much for your help