Answer: 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.
