Question

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what is f(x) when x=6?

Explanation:

Step1: Identify the function type

The graph is a straight line, so it's a linear function. Let's assume the linear equation is \( f(x)=mx + b \).

Step2: Find two points

From the graph, when \( x = 0 \), \( f(0)=2 \) (so \( b = 2 \)). When \( x = 10 \), \( f(10)=6 \).

Step3: Calculate the slope \( m \)

Using the slope formula \( m=\frac{f(10)-f(0)}{10 - 0}=\frac{6 - 2}{10}=\frac{4}{10}=0.4 \).

Step4: Write the equation

So \( f(x)=0.4x + 2 \).

Step5: Substitute \( x = 6 \)

\( f(6)=0.4\times6+2=2.4 + 2 = 4.4 \)? Wait, maybe the grid is with integer steps. Let's check the graph again. If at \( x = 0 \), \( y = 2 \); at \( x = 5 \), maybe \( y = 4 \) (since from (0,2) to (10,6), the rise over run is 4 over 10, so per 5 units x, y increases by 2). So at \( x = 5 \), \( y = 4 \), then at \( x = 6 \), let's see the slope. From (0,2) to (10,6), the slope is \( \frac{6 - 2}{10 - 0}=\frac{4}{10}=\frac{2}{5} \). So \( f(6)=\frac{2}{5}\times6+2=\frac{12}{5}+2=\frac{12 + 10}{5}=\frac{22}{5}=4.4 \)? But maybe the graph has integer coordinates. Wait, maybe the points are (0,2) and (10,6), so the equation is \( y=\frac{2}{5}x + 2 \). When \( x = 6 \), \( y=\frac{12}{5}+2 = 4.4 \), but maybe the graph is such that each grid square is 1 unit. Wait, maybe I misread. Let's count the grid. From x=0 (y=2) to x=10 (y=6), so the line goes from (0,2) to (10,6). So the change in y is 4, change in x is 10, so slope 4/10=2/5. So at x=6, y=2 + (2/5)6=2 + 12/5=22/5=4.4. But maybe the answer is 4.4 or 22/5. Alternatively, maybe the graph is with x=0, y=2; x=5, y=4; x=10, y=6. So at x=5, y=4, so the slope is (4-2)/(5-0)=2/5. So at x=6, y=4 + (2/5)(1)=4.4. But maybe the problem expects integer. Wait, maybe the graph is different. Wait, the original graph: let's see, the y-axis has marks at 2,4,6. The x-axis at 0,2,4,6,8,10. So when x=0, y=2; x=10, y=6. So the line passes through (0,2) and (10,6). So the equation is y = 0.4x + 2. So when x=6, y=0.4*6 + 2=2.4 + 2=4.4. But maybe the answer is 4.4 or 22/5. But maybe the graph is drawn with each x unit, y increases by 0.4. So the answer is 4.4.

Wait, maybe I made a mistake. Let's check again. The two points are (0,2) and (10,6). So the slope m=(6-2)/(10-0)=4/10=2/5. So the equation is y= (2/5)x + 2. Plugging x=6: y= (2/5)*6 + 2= 12/5 + 10/5=22/5=4.4. So f(6)=4.4.

Answer:

\( 4.4 \) (or \( \frac{22}{5} \))