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25 votes
25 votes
HELP

The line y = —o.5x + b passes through the points (1, 5.5), (3, p), (4, 4), and (7, n). Find b, n, and p.

HELP The line y = —o.5x + b passes through the points (1, 5.5), (3, p), (4, 4), and-example-1
User Adam Cobb
by
3.1k points

2 Answers

21 votes
21 votes

Answer:

b = 6

p = 4.5

n = 2.5

Explanation:

User Mike Hixson
by
2.8k points
10 votes
10 votes

Answer:

b = 6

p = 4.5

n = 2.5

Explanation:

The equation of the given line is

y = 0.5x + b (1)

To find b, take the (x, y) coordinates of any known point through which the line passes, plugin x and y values of that point and solve for b

The line passes through (4, 4) so x = 4 and y =4

Plugging these values into the line equation (1) gives

4 = -0.5(4) + b

4 = -2 + b

Switch sides

-2 + b = 4

Add 2 to both sides

-2 + b +2 = 4 + 2

b = 6

So the equation of the line is

y = -0.5x + 6 (2)

We can verify this by plugging in x, y values for another known point and see that the computed value of y agrees with the known values

Taking point (1, 5.5) with x = 1 and y = 5.5

y = -0.5(1) + 6 = -0.5 + 6 = 5.5

So the computed y value of 5.5 agrees with the given value of y

To compute for unknown p use the line equation (2) and solve for p

y = -0.5x + 6

Use the point (3, p)

p = -0.5(3) + 6

p = -1.5 + 6 = 4.5

So p = 4.5

Use point (7,n) plug in value of x for that point and solve for n

n = -0.5(7) + 6 = -3.5 + 6 = 2.5

So n = 2.5

The 4 points through which the line passes are

(1, 5.5) given

(3, 4.5) computed

(4, 4) given

(7, 2.5) computed

The attached graph shows the line and the 4 points

HELP The line y = —o.5x + b passes through the points (1, 5.5), (3, p), (4, 4), and-example-1
User Liman
by
3.1k points