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Video: Comparing the Rates of Change of Two Given Linear Functions

Bethani Gasparine

Determine which of the given functions has a greater rate of change? [A] 𝑦 = 5𝑥 + 2 [B] a function where the input is multiplied by 2.

01:16

Video Transcript

Determine which of the given functions has a greater rate of change. Our first function is a linear function. Itโ€™s in the form of ๐‘ฆ equals ๐‘š๐‘ฅ plus ๐‘, where ๐‘š is your slope and ๐‘ is your ๐‘ฆ-intercept. Now the slope is your rate of change, so here the rate of change would be five or five over one.

Option B says itโ€™s a function where the input is multiplied by two. So when you have a function, thereโ€™s an input and thereโ€™s an output. The input is what you plug in. Thatโ€™s ๐‘ฅ. The output is the answer that pops out. Thatโ€™s ๐‘ฆ. So again, this is a function where the input is multiplied by two, so ๐‘ฆ equals two ๐‘ฅ. This is another linear function, because itโ€™s in the form ๐‘ฆ equals ๐‘š๐‘ฅ plus ๐‘.

Now there isnโ€™t a ๐‘ that just means ๐‘ is zero. So here the rate of change or the slope is two. So out of either A or B, which one has a greater rate of change? That would be option A: ๐‘ฆ equals five ๐‘ฅ plus two. Because its rate of change is five over one where Bโ€™s rate of change is two over one, which is less.