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