Let * denote the multiplication symbol. i.e. when we say 3*2, we are multiplying 3 by 2 and obtaining 6.
A linear function is given in the following form:
f(x) = a*x + b
where a and b are real numbers, x is the independent variable and f(x) (otherwise referred to as y) is the dependent variable.
So, we need to come up with a linear function f(x) = a*x + b which satisfies the following criterion:
f(0) = -5 and f(1) = -3.
If f(0) = -5, then this means that f(x) = -5 when x = 0.
So, f(0) = -5 = a*0 + b = 0 + b. So -5 = 0 + b, and therefore b = -5.
Now we know our function is equal to f(x) = ax + (-5) = ax - 5.
We need f(x) to equal -3 when x = 1. Let's plug in 1 for x:
f(1) = a*1 - 5 = a - 5. Once again, we need f(1) = -3, so:
a - 5 = -3 --> a = -3 + 5 --> a = 2. So now we have solved for both a and b, a = 2 and b = -5.
Plugging in 2 and -5 into our original linear function f(x) = a*x + b, we obtain:
f(x) = 2*x - 5. This is the solution.
Hope this helps. Leave a rating please! and feel free to ask any questions.
