Question

1. the table represents some points on the graph of linear function f.

x	2	4	7	10
f(x)	20	30	45	60

which function represents f?
choose the correct answer from each drop down menu to write the function.
$f(x) = \boldsymbol{\text{-- choose the correct answer --}} x + \boldsymbol{\text{-- choose the correct answer --}}$

Explanation:

Step1: Find the slope (m)

The formula for slope between two points \((x_1, y_1)\) and \((x_2, y_2)\) is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Let's take the first two points \((2, 20)\) and \((4, 30)\). Then \(m=\frac{30 - 20}{4 - 2}=\frac{10}{2} = 5\).

Step2: Find the y - intercept (b)

The equation of a line is \(y=mx + b\) (here \(y = f(x)\)). We know \(m = 5\) and we can use the point \((2, 20)\). Substitute \(x = 2\), \(y = 20\) and \(m = 5\) into \(y=mx + b\): \(20=5\times2 + b\). Simplify: \(20 = 10 + b\). Subtract 10 from both sides: \(b=20 - 10=10\).

Step3: Write the function

So the function \(f(x)=5x + 10\).

Answer:

\(f(x)=\boldsymbol{5}x+\boldsymbol{10}\)