Mathematics, 20.10.2021 05:10 suhailalitariq

The line y=−0.5x+b passes through the points (1,5.5), (3,p), (4,4), and (7,n). Find b, n, and p.

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Answer from: yaniravivas79

b = 6; n = 2.5; p = 4.5

Step-by-step explanation:

Finding b

If we use the given slope and use one of the points to write the equation in point-slope form (y - y₁) = m(x - x₁)), we can rearrange it to find the y-intercept:

Using (4,4)

⇒ y - 4 = - 0.5 (x - 4)

y - 4 = - 0.5 x + 2

y = -0.5 x + 6

∴ b = 6

Calculating 'n' and 'p'

We can find n and p by plugging the points into the newly found equation y = -0.5 x + 6.

For n using (7, n)

since y = -0.5 x + 6

n = -0.5 (7) + 6

∴ n = 2.5

For p using (3,p)

since y = -0.5 x + 6

p = - 0.5 (3) + 6

p = - 1.5 + 6

p = 4.5

Checking the answer

We can check the answer we got in two ways:

We could also have found n a different way:

Using the points (4, 4) and (7, n) as (x₁, y₁) & (x₂, y₂) respectively

The slope of the line (m) = (y₂ - y₁) ÷ (x₂ - x₁)

- 0.5 = (n - 4) ÷ (7 - 4)

- 0.5 = ⁿ⁻⁴/₃ [multiply both sides by 3]

- 1.5 = n - 4 [add four to both sides]

n = 2.5 [this matches the value of n we found]

We can plot the line and see if it goes through the points we found. As seen in the graph below, the line passes through all the points.

The line y=−0.5x+b passes through the points (1,5.5), (3,p), (4,4), and (7,n). Find b, n, and p.

Answer from: Quest

none cuz there are no "following statements" regarding the question

step-by-step explanation:

Answer from: Quest

step-by-step explanation:

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The line y=−0.5x+b passes through the points (1,5.5), (3,p), (4,4), and (7,n). Find b, n, and p....

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