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.

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

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

For p using (3,p)

               since y = -0.5 x + 6

                         p = - 0.5 (3) + 6

                         p = - 1.5 + 6

Checking the answer

We can check the answer we got in two ways:

         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]

there is no grid

step-by-step explanation: