Example Equation: y=3/16x+1.75 Interpretation: See solution.
Practice makes perfect
To write an equation that models the roasting time as a function of the weight of a turkey, we will first draw a line that appears to fit the given data closely. There should be approximately as many points above the line as below it.
Now, we can start to write an equation for the line of fit. Notice that the points (20,5.5) and (12,4) lie on the line. With these points, we can find the slope of the line by using the Slope Formula.
We found that the slope of the line is 316. Next, we will find the y-intercept of the line. Therefore, we should write the equation in slope-intercept form, y= mx+ b, where m is the slope and b is the y-intercept.
y= 3/16x+ b
By substituting either of the points on the line into the above equation, we can find b. Let's substitute (12,4)!
With this, we can complete the equation.
y= 3/16x+ 1.75
In this context, since the slope is positive, the roasting time increases as the turkey's weight increases. Now, since the slope is given in hours, let's multiply it by 60 to convert it into minutes. This will help us to have a clearer idea about how the roasting time increases.
3/16*60 ⇒ 11.25 minutes
Therefore, the roasting time increases 11.25 minutes for each pound of turkey. On the other hand, because there cannot be any roasting time for 0-pound of turkey, the y-intercept of 1.75 does not make sense.
