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.
1 answer:
Answer:y = -0.5x + 6
n = 4.5
p = 2.5
Step-by-step explanation:
Tough one. It is easy to get discouraged, but let's take a look.
We'll assume this is a straight line, with the form y=mx+b, where m is the slope and b is the y-intercept (the value of y when x=0). We're given the following points:
(1, 5.5)
(3, p)
(4, 4). and
(7, n)
We have two points that are honest-to-good numbers, no pesky letters:
(1, 5.5) and (4, 4)
We can use these two points to find the slope AND b, the y-intercept.
Slope is Rise/Run:
Going from (1, 5.5) to (4, 4).
The Rise is (4 - 5.5) or -1.5.
The Run is (4-1) or 3
The Rise/Run, m, is -1.5/3, or -0.5.
That gives us: y = -0.5x+b
Use one of the two points to find b. I'll use (4,4):
y = -0.5x+b
4 = -0.5*(4)+b
4 = -2 + b
b = 6
The equation is y = -0.5x + 6
Now let's take the two other points: (3,p) and (7,n), Since we have the equation, we can use the one value to generate the second:
(3,p)
If x=3:
y = -0.5x + 6
y = -0.5*(3) + 6
y = 4.5
The point is (3,4.5) and n = 4.5
The other point: (7,n)
y = -0.5x + 6
y = -0.5*(7) + 6
y = -3.5+6
y = 2.5
The point is (7, 2.5) p = 2.5
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