janice noticed that the number of problems she did for homework (x) formed a linear relationship with her quiz score (y). When she did 3 problems she earned a 25% and when she did 8 problems she earned a 60%. Write an equation to represent this situation.
To write an equation representing the linear relationship between the number of problems (x) and the quiz score (y), we need to find the equation of a line in slope-intercept form, which is given by y = mx + b, where m represents the slope, and b represents the y-intercept.
First, let's find the slope (m). We can calculate the change in y divided by the change in x between any two points on the line.
The change in y is 60 - 25 = 35, and the change in x is 8 - 3 = 5.
So the slope (m) is 35/5 = 7.
Now, let's find the y-intercept (b) by substituting the values of one point on the line into the equation y = mx + b.
We'll use the point (3, 25), where x = 3 and y = 25.
Substituting these values into the equation, we get 25 = 7(3) + b.
Simplifying this equation, we have 25 = 21 + b.
To isolate b, we subtract 21 from both sides of the equation, which gives us b = 25 - 21 = 4.
Thus, the equation representing Janice's situation is y = 7x + 4.