Question

11 mark for review
x | 10 | 15 | 20 | 25
f(x) | 82 | 137 | 192 | 247
the table shows four values of x and their corresponding values of f(x). there is a linear relationship between x and f(x) that is defined by the equation f(x) = mx - 28, where m is a constant. what is the value of m?

Explanation:

Step1: Choose a pair (x, f(x))

Take \( x = 10 \), \( f(x)=82 \) from the table.

Step2: Substitute into the equation

Substitute into \( f(x)=mx - 28 \): \( 82 = 10m - 28 \).

Step3: Solve for m

Add 28 to both sides: \( 82 + 28 = 10m \), so \( 110 = 10m \). Divide by 10: \( m = \frac{110}{10}=11 \). (We can verify with other pairs, e.g., \( x = 15 \), \( f(x)=137 \): \( 137 = 15m - 28 \), \( 15m = 165 \), \( m = 11 \), which matches.)

Answer:

11