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CCSS.Math: ,

F is a linear function whose table of values is shown below so they give us different values of X and what the function is for each of those X's which graphs show functions which are increasing at the same rate as F so how what is the rate at which F is increasing when x increases by four we have our function increasing by seven so we could just look for which of these lines are increasing at a rate of 7/4 seven in the vertical direction every time we move four in the horizontal direction an easy way to eyeball that would actually be just to plot two points for F and then see what that rate looks like visually so if we see here when x is zero f is negative 1 when x is zero when x is zero f is negative 1 so when x is zero f is negative 1 and when X is 4 f is 6 when X is 4 f is 6 so 1 2 3 4 5 6 so just like that and two points specify a line we know that it is a linear linear function you could even verify here would be increased by 4 again we increase our function by 7 again we know that these two points are on f and so we get a sense of the rate of change of f and when you draw it like that it immediately becomes pretty clear which of these has the same rate of change of f a is increasing faster than f c is decrease increase it is C is increasing slower a is increasing much faster than F C is increasing slower than F B is decreasing so that's not even even close but D seems to have the exact same inclination the exact same slope the exact same slope as f so D is what we would go with and we can even verify it even if we didn't even if we didn't draw it in this way our change our change in F for a given change in X is equal to when X changed plus for our function change plus 7 it is equal to 7/4 and we can verify that on D if we increase in the x-direction by four so we go from four to eight then in the vertical direction we should increase by seven so one two three four five six seven and it indeed does increase at the exact same rate