Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.

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 + 8(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. It’s in the form of 𝑦 equals π‘šπ‘₯ plus 𝑏, where π‘š 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 π‘₯. 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 π‘₯. This is another linear function, because it’s in the form 𝑦 equals π‘šπ‘₯ 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 π‘₯ plus two. Because its rate of change is five over one where 𝑏’s rate of change is two over one, which is less.