How would you find y=mx+b when given (5,8) and (10, 14)?

Answer 1
In general, the slope of a line joining points #(x_1,y_1)# and #(x_2,y_2)# is #m = (y_2 - y_1)/(x_2 - x_1)#
For the given values #(x_1,y_1) = (5,8)# and #(x_2,y_2) = (10,14)# we have #m = (14- 8)/(10-5) = 6/5#
Using (arbitrarily) #(x_1,y_1) = (5,8)# as a point and (not arbitrarily) #m=6/5# as the slope
The slope-point formula for the line can be written as #(y-8) = 6/5(x-5)#
#rarr 5y - 40 = 6x - 30# #rarr 5y = 6x +10#
We can convert this to slope-intercept form #y=mx+b# by dividing both sides by #5#
#y = 6/5x + 2#
The slope is #6/5# and the y-intercept is #2#
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Answer 2

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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Answer 3

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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Answer from HIX Tutor

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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