1. **Problem Statement:** We are given a table of time $t$ (in hours) and distance $d$ (in kilometers) for Paul's drive from Vancouver to Kelowna. We need to graph the linear relation and find how far Paul drove in the first 2 hours. 2. **Understanding the Data:** The table shows pairs $(t, d)$: $$ \begin{array}{c|c} \text{Time } t (h) & \text{Distance } d (km) \\ \hline 0.5 & 45 \\ 0.9 & 81 \\ 1.2 & 108 \\ 1.5 & 135 \\ 2.3 & 207 \\ 2.7 & 243 \\ 3.5 & 315 \end{array} $$ 3. **Step 1: Graph the linear relation.** - The horizontal axis (x-axis) is time $t$ in hours. - The vertical axis (y-axis) is distance $d$ in kilometers. - Plot each point $(t, d)$ from the table. - Connect the points with a straight line since the relation is linear. 4. **Step 2: Find the linear equation.** - Use two points to find the slope $m$: $$ m = \frac{d_2 - d_1}{t_2 - t_1} = \frac{81 - 45}{0.9 - 0.5} = \frac{36}{0.4} = 90 $$ - The slope $m=90$ means Paul drives 90 km per hour. - Use point-slope form with point $(0.5, 45)$: $$ d - 45 = 90(t - 0.5) $$ - Simplify: $$ d = 90t - 45 + 45 = 90t $$ So the linear equation is: $$ d = 90t $$ 5. **Step 3: Calculate distance driven in first 2 hours.** - Substitute $t=2$ into the equation: $$ d = 90 \times 2 = 180 $$ **Answer:** Paul drove 180 kilometers in the first 2 hours.