How would you find y=mx+b when given (5,8) and (10, 14)?
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To find the equation of a line (y=mx+b) when given two points, (x₁, y₁) and (x₂, y₂), you can use the slope-intercept form formula:
m = (y₂ - y₁) / (x₂ - x₁)
Once you have the slope (m), you can plug it into the formula and solve for b:
b = y₁ - mx₁
Using the points (5,8) and (10,14):
m = (14 - 8) / (10 - 5) m = 6 / 5
Now, substitute one of the points and the slope into the formula to find b:
8 = (6/5)(5) + b 8 = 6 + b b = 8 - 6 b = 2
So, the equation of the line is:
y = (6/5)x + 2
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To find the equation of a line in slope-intercept form ((y = mx + b)) given two points, ((x_1, y_1)) and ((x_2, y_2)), you first need to determine the slope ((m)) using the formula:
[m = \frac{y_2 - y_1}{x_2 - x_1}]
Once you have the slope, you can plug it into the equation (y = mx + b) along with one of the points to solve for the y-intercept ((b)). After finding (b), you can write the equation of the line.
Given the points ((5,8)) and ((10,14)), we can find the slope:
[m = \frac{14 - 8}{10 - 5} = \frac{6}{5}]
Now, we have the slope ((m = \frac{6}{5})). We can choose any of the given points to find the y-intercept. Let's use ((5,8)):
[8 = \frac{6}{5} \times 5 + b] [8 = 6 + b] [b = 8 - 6 = 2]
Now that we have (m = \frac{6}{5}) and (b = 2), we can write the equation of the line:
[y = \frac{6}{5}x + 2]
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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
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