Answers

1. Answer:

   The equation that represents the line of Paul’s grade downfall is:

   y = (-20)x + 130

   This equation states that for every decrease of 1 in the value of x (representing the number of weeks), the value of y (representing Paul’s math average) decreases by 20.

   Step-by-step explanation:

   To find the equation that represents the line of Paul’s grade downfall, we can use the two given points to plot the line on a coordinate plane. The point (2, 90) represents the value that after 2 weeks, Paul’s math average is 90, and the point (4, 50) represents the value that after 4 weeks, Paul’s grade has dropped to 50. We can plot these two points on the coordinate plane as follows:

   (2, 90)

   (4, 50)

   To find the equation of the line that passes through these two points, we can use the slope-intercept form of a linear equation, which is y = mx + b, where m is the slope of the line and b is the y-intercept.

   To find the slope of the line, we can use the formula:

   m = (y2 – y1) / (x2 – x1)

   Substituting the coordinates of the two points, we get:

   m = (50 – 90) / (4 – 2)

   = -40 / 2

   = -20

   To find the y-intercept of the line, we can substitute the coordinates of one of the points and the slope into the slope-intercept form of the equation:

   y = mx + b

   Substituting the coordinates of the point (2, 90) and the slope of -20, we get:

   90 = (-20)(2) + b

   = -40 + b

   = b – 40

   Solving for b, we get:

   b = 90 + 40

   = 130

   Reply