To predict a day when they both have the same number of signatures (and the number of signatures that will be), we have to set up two functions representing each of their signature growth.
So Valeria has 26 signatures as her starting point, and 6 signatures a day (x) as her rate. In slope-intercept (y = mx + b) form, this would be written y = 6x + 26, with y being the total number of signatures on x day.
Christina has 53 signatures as her starting point, and 3 signatures a day (x) as her rate. In slope-intercept (y = mx + b) form, this would be written y = 3x + 53, with y being the total number of signatures on x day.
To figure out how many days would it take to have the same amount of signatures, meaning the same y values, we have to set the equations equal to each other (bc each have the same y value as the other so they basically equal each other). That would mean:
6x + 26 = 3x + 53
To simplify this, get the numbers to one side and the xs to another by subtracting 3x and 26 from both sides. This would make it:
3x = 27, in which we can divide both sides by 3 to get x = 9. So the number of days after which they would have the same amount of signatures would be 9.
Now since we know the shared x value, we just plug it into one of the equations to get the resulting y value. I’ll pick Christina’s.
y = 6(9) + 26, which is 54 + 26, which is 80. So the number of signatures they both will have when they reach the same number is 80.
Hope this helps.