Question 1119942
it bears 3 more fruits every year.


it bore 12 in 1995.


how many will it bear in 2010.


2010 - 1995 = 15 years.


15 * 3 = 45


it will bear 12 + 45 = 57 fruits in 2010.


if you let x equal the number of years, then your equation becomes:


y = 3x + 12


if you let 1995 represent year 0, then 2010 will represent year 15 because 1995 + 15 = 2010.


basically, you just add 1995 to x to find the year that it represents.


x = 0, the year is 1995.
x = 15, the year is 1995 + 15 = 2010.


you can graph the equation of y = 3x + 12.


it looks like this:


<img src = "http://theo.x10hosting.com/2018/071605.jpg" alt="$$$" >


you can also let x represent the year, although this equation is a littler more cumbersome to graph and represent.


in that case, the equation becomes y = 3 * (x - 1995) + 12


that graph looks like this:


<img src = "http://theo.x10hosting.com/2018/071606.jpg" alt="$$$" >


what you have done is shifted the graph horizontally 1995 units to the right.


when x is 1995, (x-1995) is equal to 0.


the equation then becomes y = 0 + 12 which results in y = 12.


when x is 2010, (x-1995) is equal to 15.


the equation then becomes y = 3 * 15 + 12 which results in y = 57.


both forms get you the same value of y.


the fact that you have the same increase year makes the equation a linear equation of the form y = mx + b.


m is the slope.
b is the y-intercept.


the slope is 3 in both equations because the increase is 3 units each year.


the y-intercept in the first equation is found by making x = 0 and solving for y.


y = 3x + 15 results in y = 15 when x = 0.


that's the y-intercept for the first equation.


the y-intercept for the second equation is found the same way.


y = 3 * (x - 1995) + 12 results in y = 3 * -1995) + 12 which results in y = -5973 when x = 0.


that's the y-intercept in the second equation.


the first form of the equation is the preferred form, although the second form is still valid.


here's the graph of the y-intercept of the first equation.


<img src = "http://theo.x10hosting.com/2018/071607.jpg" alt="$$$" >


here's the graph of the y-intercept of the second equation.


<img src = "http://theo.x10hosting.com/2018/071608.jpg" alt="$$$" >