Question

Use a table of values to graph the equation. $$3 x+4 y=20$$

Short answer

The graph of the equation \(3 x + 4 y = 20\) is a straight line that passes through the points (-2, 6.5), (0, 5), (2, 3.5), (4, 2), and (6, 0.5), which are obtained by substituting different x-values into the equation and solving for y.

Step-by-step solution

Choosing Values for x

Choose different values for \(x\). For this exercise, take five values (-2, 0, 2, 4, and 6)

Solve for Corresponding y Values

Substitute the chosen \(x\) values into the equation and solve for \(y\). The equation will look something like this: \(4y = 20 - 3x\) which simplifies to \(y = 5 - \frac{3}{4}x\).

Fill the Table

Create a table and fill it with the chosen \(x\) values and their corresponding \(y\) values. The table will look something like this: \[\begin{array}{|c|c|} \hline x & y \\ \hline -2 & 6.5 \\ 0 & 5 \\ 2 & 3.5 \\ 4 & 2 \\ 6 & 0.5 \\ \hline \end{array}\]

Plot the Points

Use the pairs (x, y) in the table to plot points on the graph: (-2, 6.5), (0, 5), (2, 3.5), (4, 2), and (6, 0.5). Then, draw a line that passes through all the points. This line graphically represents the equation.

Validate Your Graph

Choose another point that is not on your table, substituting those values for \(x\) and \(y\). If the numbers satisfy the equation, then your graph should be correct.