Question

For each equation, (a) give a table with at least three ordered pairs that are solutions, and (b) graph the equation. See Examples 3 and 4.2x + 3y = 5

Accepted Answer

Rewrite the given linear equation $$2x + 3y = 5 to $$express $$y in $$terms of $$x. $$This will help in finding ordered pairs. To do this, isolate $$y$$: $$3y = 5 - 2x$$, so $$y = \frac{5 - 2x}{3}. $$Choose at least three different values for $$x. $$For each chosen $$x$$ value, substitute it into the expression for $$y to $$find the corresponding $$y$$ value. This will give you ordered pairs $$(x, y)$$ that satisfy the equation. For example, if you pick $$x = 0$$, substitute into $$y = \frac{5 - 2(0)}{3} = \frac{5}{3}. So $$one ordered pair is $$(0, \frac{5}{3}). $$Repeat this for two more values of $$x ($$like $$x=3$$ and $$x=-3) to $$get at least three ordered pairs. Once you have the ordered pairs, create a table listing the $$x$$ values and their corresponding $$y$$ values. This table clearly shows the solutions to the equation. To graph the equation, plot the ordered pairs on the coordinate plane. Then, draw a straight line through these points because the equation represents a linear function. This line is the graph of the equation $$2x + 3y = 5.$$

For each equation, (a) give a table with at least three ordered pairs that are solutions, and (b) graph the equation. See Examples 3 and 4.
2x + 3y = 5

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Concetti chiave

Linear Equations in Two Variables

Finding Ordered Pairs (Solutions)

Graphing Linear Equations