3. 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.
a. What is the rate of change between points A and B?
b. What is the rate of change between points C and D?
c. Write the equation of the line that passes through the points.
Please help
slope AB = (3-0)/(2-0) = 3/2
slope CD = (12-6)/(8-4) = 6/4 = 3/2
point (0,0) tells me the y-intercept is 0
equation : y = (3/2)x = 0
or
y = (3/2)x
poorly constructed question. Just because C and D also have a slope of 3/2, does not mean that all 4 points lie on the same line
e.g. suppose they had been C(4,5) and D(6,8)
the slope would also be 3/2 , but neither point lies on y = (3/2)x
wait a minute these teacher thingys can actually sound smart??????????
To find the rate of change between two points, you can use the formula:
Rate of Change = (Change in Y) / (Change in X)
a. For points A(0, 0) and B(2, 3):
Change in Y = 3 - 0 = 3
Change in X = 2 - 0 = 2
Rate of Change = 3 / 2 = 1.5
So, the rate of change between points A and B is 1.5.
b. For points C(4, 6) and D(8, 12):
Change in Y = 12 - 6 = 6
Change in X = 8 - 4 = 4
Rate of Change = 6 / 4 = 1.5
So, the rate of change between points C and D is also 1.5.
c. To write the equation of the line that passes through the points, you can use the slope-intercept form:
y = mx + b
To find the slope (m), you can use any two points on the line:
m = (Change in Y) / (Change in X)
For points A(0, 0) and B(2, 3):
m = 1.5 (as calculated before)
Now, to find the y-intercept (b), you can substitute the coordinates of one of the points (let's use point B):
3 = 1.5(2) + b
3 = 3 + b
b = 0
Therefore, the equation of the line that passes through the points A and B is:
y = 1.5x
Hope this helps! Let me know if you have any further questions.