Let's solve the problem step-by-step.
Given the equation of the function:
[tex]\[ y = 4x - 1.5 \][/tex]
We need to find the values of [tex]\( y \)[/tex] for different given values of [tex]\( x \)[/tex].
### Part (a): When [tex]\( x = 12 \)[/tex]
Substitute [tex]\( x = 12 \)[/tex] into the equation:
[tex]\[ y = 4(12) - 1.5 \][/tex]
[tex]\[ y = 48 - 1.5 \][/tex]
[tex]\[ y = 46.5 \][/tex]
So, when [tex]\( x = 12 \)[/tex], [tex]\( y = 46.5 \)[/tex].
### Part (b): When [tex]\( x = 2.5 \)[/tex] (Note that [tex]\( 2 \frac{1}{2} = 2.5 \)[/tex])
Substitute [tex]\( x = 2.5 \)[/tex] into the equation:
[tex]\[ y = 4(2.5) - 1.5 \][/tex]
[tex]\[ y = 10 - 1.5 \][/tex]
[tex]\[ y = 8.5 \][/tex]
So, when [tex]\( x = 2.5 \)[/tex], [tex]\( y = 8.5 \)[/tex].
### Part (c): When [tex]\( x = -0.5 \)[/tex] (Note that [tex]\( -\frac{1}{2} = -0.5 \)[/tex])
Substitute [tex]\( x = -0.5 \)[/tex] into the equation:
[tex]\[ y = 4(-0.5) - 1.5 \][/tex]
[tex]\[ y = -2 - 1.5 \][/tex]
[tex]\[ y = -3.5 \][/tex]
So, when [tex]\( x = -0.5 \)[/tex], [tex]\( y = -3.5 \)[/tex].
### Summary
(a) When [tex]\( x = 12 \)[/tex], [tex]\( y = 46.5 \)[/tex].
(b) When [tex]\( x = 2.5 \)[/tex], [tex]\( y = 8.5 \)[/tex].
(c) When [tex]\( x = -0.5 \)[/tex], [tex]\( y = -3.5 \)[/tex].
