Determine which of the given functions has a greater rate of change. Our first function is a linear function. It’s in the form of 𝑦 equals 𝑚𝑥 plus 𝑏, where 𝑚 is your slope and 𝑏 is your 𝑦-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 it’s a function where the input is multiplied by two. So when you have a function, there’s an input and there’s an output. The input is what you plug in. That’s 𝑥. The output is the answer that pops out. That’s 𝑦. So again, this is a function where the input is multiplied by two, so 𝑦 equals two 𝑥. This is another linear function, because it’s in the form 𝑦 equals 𝑚𝑥 plus 𝑏.
Now there isn’t a 𝑏 that just means 𝑏 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: 𝑦 equals five 𝑥 plus two. Because its rate of change is five over one where B’s rate of change is two over one, which is less.