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irina [24]
3 years ago
5

Write the equation of the line that passes through the given points (9,4) and (2,13)

Mathematics
1 answer:
iris [78.8K]3 years ago
3 0

Answer:

y = -9 / 7x + 109 / 7

Step-by-step explanation:

To find the equation of any line, you must find the slope and y-intercept (when writing in slope-intercept form). In this case, we can find both of these values by using the two coordinate pairs that are given:

Slope - the change in y over the change in x

  1. 9 / -7 = -9 / 7
  2. slope = -9 / 7
  3. y-intercept - when x = 0

Right now, since we have the slope, we know the equation will look like this: y = -9 / 7x + b, b is what we are trying to find, the y-intercept. To find b, we can substitute a given coordinate pair that we know will fit this line and then solve:

  1. 13 = -9 / 7 x 2 + b
  2. 13 = -18 / 7 + b
  3. 91 / 7 + 18 / 7 = b
  4. 109 / 7 = b

After finding both the slope and y-intercept, we can now combine them together to form the equation of the line:

y = -9 / 7x + 109 / 7

Hope this helps!!

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2. 3/4(-4 + 4x) = -3 + 3x   3/4 times 4 is 3, so if you distribute 3/4 (-4 + 4x), you will get -3 + 3x. 

3. -0.113(-4x - 4) = 0.452x + 0.452   0.113 times 4 is 0.452, but you need to make sure to have the correct signs. Since the product is positive and -0.113 is negative, you would have to multiply it by a negative to get the product.

If you're having trouble with multiplying by fractions, just use repeated addition in your head. For example, for the first problem, instead of trying to tackle 3/4 times 4, think 3/4 + 3/4 + 3/4 + 3/4.

3/4 + 3/4 = 6/4
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For the second problem, when multiplying by a decimal, just do what you'd normally do for multiplication. When you get to the end, count how many digits you had behind the decimal before, and put the decimal in the corresponding space for the answer.

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0452

There are 3 digits behind the 0 in 0.113, so there should be 3 digits behind the decimal in the answer. So, the answer should be 0.452.

Hope this helps!
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