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write a function rule given the table shown below so how can we do this well first we need to establish what kind of function we have and looking at the the numbers for x and y we could see it's a linear function whenever x increases by one y increases by three so because we have a constant change for y for every constant change for x we know we're dealing with a linear function therefore we could use this equation y equals mx plus b that's the function of that's the equation for a linear function in slope-intercept form now the first thing we want to do is you want to calculate the slope the slope is going to be the change in y over the change in x and notice that the slope is constant every time x increases by one y changes by three so for every change in one in the x values there's a change of positive three in the y values so the slope is 3. so that's our m value b is the y-intercept so b is the y-value when x is 0. when x is zero y is two so the y intercept is two so all we need...