Interpreting Linear and Exponential Functions Arising in Applications
Christian is making apple pies for all his friends and family. He has made 10 pies for his family to taste test. He is also planning on giving out 3 pies to each friend and family member.
Linear Function
y= 3x + 10
To describe this function, we will start of with the "3x". The "3" represents the number of pies he plans on giving to each family member and friend and the "x" represents the number of family and friends he will be giving them to. Since we don't know how many family members he is giving them to, the variable x will represent the value. The "3x" would represent the slope if it were graphed. Next, the "10" in the equation, represents how many he will make for his family to taste test. If this was graphed, the "10" would represent the y-intercept.
y= 3x + 10
To describe this function, we will start of with the "3x". The "3" represents the number of pies he plans on giving to each family member and friend and the "x" represents the number of family and friends he will be giving them to. Since we don't know how many family members he is giving them to, the variable x will represent the value. The "3x" would represent the slope if it were graphed. Next, the "10" in the equation, represents how many he will make for his family to taste test. If this was graphed, the "10" would represent the y-intercept.
The graph starts at (0,10), because if you plug in 0 into "x" you will get 10, this also represents the y-intercept. Also, Christian has 10 pies before he starts giving them out to friends and family. Because Christian is making pies, it is impossible to make a negative amount of pies, so he must have made at least 1 pie or none at all. The graph moves at a positive constant slope of 3. You can input any positive number and it will appear on this graph. Because Christian can't give out pies to half a family member or friend, the domain of this graph will be whole positive numbers.