Question 3.2.5: Graph the equation y = -1/3x + 2....
Graph the equation y=-\frac{1}{3} x+2.
Step 1:
To find the ordered pairs that satisfy the equation, we can start by choosing different values for x and then calculate the corresponding values of y. In this case, since the equation involves multiplying x by -1/3, it would be helpful to choose values of x that are divisible by 3, such as -3, 0, and 3.
Step 2:
For the first ordered pair, let's take x = -3. Plugging this into the equation, we have y = (-1/3)(-3) + 2 = 1 + 2 = 3. Therefore, the first ordered pair is (-3, 3).
Step 3:
For the second ordered pair, let's take x = 0. Plugging this into the equation, we have y = (-1/3)(0) + 2 = 0 + 2 = 2. Therefore, the second ordered pair is (0, 2).
Step 4:
For the third ordered pair, let's take x = 3. Plugging this into the equation, we have y = (-1/3)(3) + 2 = -1 + 2 = 1. Therefore, the third ordered pair is (3, 1).
To graph these ordered pairs, we plot the points (-3, 3), (0, 2), and (3, 1) on a coordinate plane. Then, we draw a straight line through these points. This line represents the graph of the equation y = -1/3x + 2.
Final Answer
We need to find three ordered pairs that satisfy the equation. To do so, we can let x equal any numbers we choose and find corresponding values of y. But, since every value of x we substitute into the equation is going to be multiplied by -\frac{1}{3} let’s use numbers for x that are divisible by 3, like – 3, 0, and 3. That way, when we multiply them by -\frac{1}{3} the result will be an integer.
\begin{aligned}\text { Let }~x=-3 ; \quad y & =-\frac{1}{3}(-3)+2 \\ y & =1+2 \\ y & =3 ~~~~~~~ ~~~~~~~\text { (- 3, 3) is one solution }\end{aligned}
\begin{aligned}\text { Let } x=0 ; \quad y & =-\frac{1}{3}(0)+2 \\ y & =0+2 \\ y & =2~~~~~~~ ~~~~~~~\text { (0, 2) is another solution }\end{aligned}
\begin{aligned}\text { Let } x=3 ; \quad y & =-\frac{1}{3}(3)+2 \\y & =-1+2 \\ y & =1~~~~~~ ~~~~~~~~\text { (3 , 1) is a third solution }\end{aligned}
Graphing the ordered pairs (- 3, 3), (0, 2), and (3, 1) and drawing a straight line through their graphs, we have the graph of the equation y=-\frac{1}{3} x+2.
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