Which of the following can be used to find the slope between two points? y2−y1x2−x1
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What is the rate of change between (3, 2) and (6, 10)?x2− x1y2−y1
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y = mx + b14
38
83
The correct formula to find the slope between two points is:
slope = (y2 - y1)/(x2 - x1)
Using this formula with the given points (3, 2) and (6, 10), we get:
slope = (10 - 2)/(6 - 3) = 8/3
So the rate of change (i.e. slope) between (3, 2) and (6, 10) is 8/3.
None of the answer choices provided match this result, but the formula y = mx + b is the equation of a line in slope-intercept form, where m is the slope and b is the y-intercept. So we can use the slope we just found to write an equation in this form.
y = (8/3)x + b
To find b (the y-intercept), we can plug in one of the points, say (3, 2):
2 = (8/3)*3 + b
2 = 8 + b/3
b/3 = -6
b = -18
So the equation of the line passing through (3, 2) and (6, 10) is:
y = (8/3)x - 18
To find the slope between two points (x1, y1) and (x2, y2), you can use the formula:
slope = (y2 - y1) / (x2 - x1)
For the first question:
Given the points (2, -1) and (2, -1), plug the values into the formula:
slope = (-1 - (-1)) / (2 - 2)
= 0 / 0
Since the numerator and denominator are both zero, this slope is undefined.
For the second question:
Given the points (3, 2) and (6, 10), plug the values into the formula:
slope = (10 - 2) / (6 - 3)
= 8 / 3
Therefore, the rate of change between (3, 2) and (6, 10) is 8/3.
For the third question:
The equation y = mx + b represents a linear equation, where m represents the slope and b represents the y-intercept.
Here the slope, m, is 14 and the y-intercept, b, is 38.
To find the slope between two points, you can use the formula:
slope = (y2 - y1) / (x2 - x1)
Let's calculate the slope using the given points:
For the first question:
x1 = 2, y1 = -1
x2 = -2, y2 = 1
slope = (1 - (-1)) / (-2 - 2)
= 2 / (-4)
= -1/2
Therefore, the slope between the two points is -1/2.
For the second question:
x1 = 3, y1 = 2
x2 = 6, y2 = 10
slope = (10 - 2) / (6 - 3)
= 8 / 3
Therefore, the slope between the two points is 8/3.
Please note that the third option "y = mx + b" is the equation of a straight line in slope-intercept form, where m represents the slope and b represents the y-intercept. It is not used to find the slope between two points.