Question

1. complete the table to show the rate of change

x y
0
1 7
2 13
3 19
4
5

Explanation:

Step1: Find the rate of change

Calculate the difference between consecutive y - values. For \(x = 1\) to \(x = 2\), \(13-7 = 6\). For \(x = 2\) to \(x = 3\), \(19 - 13=6\). So the rate of change (slope) \(m = 6\).

Step2: Find the equation of the line

Use the point - slope form \(y - y_1=m(x - x_1)\). Using the point \((1,7)\) and \(m = 6\), we get \(y-7 = 6(x - 1)\). Simplify: \(y-7=6x - 6\), so \(y=6x + 1\).

Step3: Find \(y\) when \(x = 0\)

Substitute \(x = 0\) into \(y=6x + 1\). Then \(y=6(0)+1=1\).

Step4: Find \(y\) when \(x = 4\)

Substitute \(x = 4\) into \(y=6x + 1\). Then \(y=6(4)+1=24 + 1=25\).

Step5: Find \(y\) when \(x = 5\)

Substitute \(x = 5\) into \(y=6x + 1\). Then \(y=6(5)+1=30 + 1=31\).

Answer:

When \(x = 0\), \(y = 1\); when \(x = 4\), \(y = 25\); when \(x = 5\), \(y = 31\)

The completed table is:

\(x\)	\(y\)
\(1\)	\(7\)
\(2\)	\(13\)
\(3\)	\(19\)
\(4\)	\(25\)
\(5\)	\(31\)