We want to estimate the heat index when the relative humidity is 75 percent and the temperature is 100^(∘) F by using a linear function. To do so, recall that linear functions follow a specific format.
y= mx+ b
In this form, m is the slope and b is the y-intercept. In our case, y indicates the heat index and x represents the temperature. We know that for every 1 degree increase in the temperature, the heat index rises 4^(∘) F. Then, the slope of our function is equal to 4.
y= 4x+ b
To find the y-intercept, consider that on a summer day the relative humidity is 75 percent, the temperature is 94^(∘) F, and the heat index is 124^(∘) F. We can substitute x= 94 and y= 124 into the above function and solve it for b.
Finally, we can complete our linear function.
y= 4x+( - 252) → y=4x-252
Now that we have the linear function that describes the heat index, we can estimate the heat index when the relative humidity is 75 percent and the temperature is 100^(∘) F. To do so, let's substitute x= 100 into the obtained function.
