ex2.1_2

Example

$x+2y=4$ , and then sketch the graph.

Solution

$x$ $y$ and compute the value of the remaining variable.

y=0 \quad \Longrightarrow \quad x+2(0)=4 \quad \Longrightarrow \quad (4,0)\\[0.25 in] y=-2 \quad \Longrightarrow \quad x+2(-2)=4 \quad \Longrightarrow \quad (8,-2)\\[0.25 in] x=-3 \quad \Longrightarrow \quad (-3)+2y=4 \quad \Longrightarrow \quad (-3,3.5)\\[0.25 in] x=6 \quad \Longrightarrow \quad (6)+2y=4 \quad \Longrightarrow \quad (6,-1)\\[0.25 in] y=5\quad \Longrightarrow \quad x+2(5)=4 \quad \Longrightarrow \quad (-6,5)

Now we'll take the five points we found, plot them, and draw a smooth curve through the points. Our smooth curve should generalize the behavior we expect from the set of all solutions.

The graph of a line including five labeled points