Question

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.

Answer 1

To find the value of \( b \), we can start by substituting the coordinates of the point (1, 5.5) into the equation of the line \( y = -0.5x + b \).

Substituting \( x = 1 \) and \( y = 5.5 \):

\[
5.5 = -0.5(1) + b
\]

\[
5.5 = -0.5 + b
\]

Adding 0.5 to both sides:

\[
b = 5.5 + 0.5 = 6
\]

So, \( b = 6 \).

Next, we need to find \( p \) at the point (3, \( p \)). We substitute \( x = 3 \) and \( b = 6 \) into the line equation:

\[
y = -0.5(3) + 6
\]

Calculating \( y \):

\[
y = -1.5 + 6 = 4.5
\]

So, \( p = 4.5 \).

Now, let’s find \( n \) at the point (7, \( n \)). We substitute \( x = 7 \) and \( b = 6 \):

\[
y = -0.5(7) + 6
\]

Calculating \( y \):

\[
y = -3.5 + 6 = 2.5
\]

So, \( n = 2.5 \).

To summarize, the values are:
- \( b = 6 \)
- \( p = 4.5 \)
- \( n = 2.5 \)