Question

The point (2, 90) represents the value that after 2 weeks, Paul's math average is a 90. The

point (4, 50) represents the value that after 4 weeks, Paul's grade has dropped to a 50
because he doesn't do homework and doesn't know how to log into Quizlet. What equation
represents the line of Paul's grade downfall? (5 Points)
y = -0.10x + 130
y=20x-100
y = 20x- 130
y=0.10x+90
y=-20x+90
y=-20x+130

Answer 1

The equation that represents the line of Paul's grade downfall is y = -20x + 130, which is calculated using the slope formula and the y-intercept obtained from the given points.

Step-by-step explanation:

To find the equation that represents the line of Paul's grade downfall, we need to calculate the slope using the two given points (2, 90) and (4, 50). The slope (m) is computed by taking the difference in the y-values divided by the difference in the x-values:

m = (y2 - y1) / (x2 - x1) = (50 - 90) / (4 - 2) = -40 / 2 = -20

Now that we have the slope, we can use one of the points to find the y-intercept (b). Using y = mx + b and substituting the slope and one of the points gives us:

90 = (-20)(2) + b

b = 90 + 40 = 130

So the equation of the line is y = -20x + 130, which represents the steady decline of Paul's grades over time.

Answer 2

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