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I graph the function $f(x)=3x+5$ but I don't understand what is going on with the x axis. What is the role of 3x in this function, how does it affect the line on the graph. For example, If the function was $f(x)=3+5$ the graph would have been a horizontal line on the 8 y-intercept. But when function is $f(x)=3x+5$ I cannot make any sense with what is going on on the x axis.

Graph of $f(x)=3x+5$

Graph of $f(x)=3x+5$

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In the graph only dotted point is when x = 0 then y = 5.

Similarly put some vales of x = -1, -2, 1, 2. To see different points you get and then plot graph.

You get similar graph.