## Algebra: A Combined Approach (4th Edition)

Step 1: Let $x$ = years after 2001; and $y$ = the number of contracts (It may be helpful to graph this, to visualize the growth in contracts). This gives the points (2, 15) and (8, 33); because there were 15 new contracts in 2003 (which is 2 years after 2001) and 33 new contracts in 2009 (which is 8 years after 2001). Step 2: Use this information to write out the slope of equation $m$ = $\frac{y_{2}-{y_1}}{x_{2}-x_{1}}$ $m$ = $\frac{33 - 15}{8 - 2}$ $m$ = $\frac{18}{6}$ = 3 Step 3: Next use the point-slope formula to write the equation $y$ - $y_{1}$ = $m$($x$ - $x_{1}$) $y$ - 15 = 3($x$ - 2) $y$ -15 = 3$x$ - 6 $y$ = 3$x$ + 9 Step 4: Using this equation we can predict how many new contracts there will be in 2017 to fill the point (16, $y$) $y$ = 3(16) + 9 = 57