Problem

Construct a table of solutions and then graph equ…

02:11

Problem 42 Hard Difficulty

Construct a table of solutions and then graph equation.
$y=3 x+1$

Answer

$$
\begin{array}{l}
1 \quad y=3 x+1 \\
x=1 \quad y=4 \\
x-0 \quad y=1 \\
x=1 \quad y=-2
\end{array}
$$

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Algebra

Elementary and Intermediate Algebra

Chapter 3

Graphing Linear Equations and Inequalities in Two Variables; Functions

Section 2

Graphing Linear Equations

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Video Transcript

and this problem were asked to construct a table of solutions and then graft this equation. Why equals three X plus one Now, when constructing tables of solutions, what we want to do is expel use that are close to our equal to zero and then plug us into the given equation to solve. Or why Well, that'll give us is on X and a Y value, which gives us an entire point to plot on our graph. So the numbers will choose for this problem, for this example would be negative one zero and one. Choosing these numbers makes it easier to solve for why, because their small numbers to work with when we are playing in the men. So starting with X equals negative one. What we'll do to plug that in is replaced all the exes in this equation with negative one. So why is equal to three X or negative one? Look one and I will simplify. Why is equal to negative three plus one and finally, why is equal to negative two? So for our first point, R y component will be negative too. So our whole point will be negative one comma negative to I've plotted here for our next point will plug in X equals zero. So why is equal to three X or three times zero one? Then we get that Y is equal to zero plus one. And finally we get that. Why is equal to one? So for our second point r y component will be one. So our point will be zero comma one has plotted here. Finally, we'll plug in X equals one. Why is equal to three X or three times one le one. Then we get that y is equal to three plus one. And finally, why is equal to four? So for a final point r Y component will be for and our point will be one comma for So we've created our table of solutions and we've plotted those points on our graph. In order to grasp this equation, what we something to do is draw line connecting draw a line starting from the very far left, connecting these points together and then continuing on to the very far right, And so if we were to imagine drawing it, it would look like this. So this is our craft equation, and you can see that the points line up with this line showing that these in fact are solutions to the equation

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