Consider the points
A(0,0), B(2,3), C(4,6), and D(8,12).
A student plotted the points and drew a line through the points. Then, he created a triangle using points A and B and another triangle using points C and D.
What is the rate of change between points A and B?
What is the rate of change between points C and D?
Write the equation of the line that passes through the points.
bruh moment
Answer:
a. 3/2
b. 6/4 idk if you need to simplify, but if so it would be 3/2
c. y = 3/2x
Step-by-step explanation:
a: to find the rate of change of points A and B, you just use a formula (i forgot what it's called but it looks like this) y2-y2/x2-x1
3/2-0/0= 3/2
so the rate of change = 3/2
b: again, using the same formula, y2-y2/x2-x1, but using points C and D
12/8-6/4=6/4 simplified to 3/2
c: since the line goes through the origin, (0,0), then there isn't a y-intercept
making the equation: y = 3/2x
To find the rate of change between two points, you can use the formula:
Rate of change = (Change in y)/(Change in x)
1. Rate of change between points A and B:
The coordinates of point A are (0,0), and the coordinates of point B are (2,3).
To calculate the change in y, subtract the y-coordinate of point A from the y-coordinate of point B: 3 - 0 = 3.
To calculate the change in x, subtract the x-coordinate of point A from the x-coordinate of point B: 2 - 0 = 2.
The rate of change between points A and B is: 3/2 or 1.5.
2. Rate of change between points C and D:
The coordinates of point C are (4,6), and the coordinates of point D are (8,12).
To calculate the change in y, subtract the y-coordinate of point C from the y-coordinate of point D: 12 - 6 = 6.
To calculate the change in x, subtract the x-coordinate of point C from the x-coordinate of point D: 8 - 4 = 4.
The rate of change between points C and D is: 6/4 or 1.5.
3. Equation of the line that passes through the points:
To find the equation of the line, you can use the point-slope form of the linear equation: y - y₁ = m(x - x₁), where m is the slope and (x₁, y₁) is any point on the line.
Using the rate of change calculated between points A and B, we know that the slope of the line passing through A and B is 1.5.
Since point A (0,0) lies on the line, we can substitute its coordinates into the point-slope form:
y - 0 = 1.5(x - 0)
y = 1.5x
Thus, the equation of the line passing through points A and B is y = 1.5x.