Graph the equation of the relation using a solid line, and then graph the inverse of the relation using a dashed line.
-$$y = 2 + 3 x$$

Question

Quizplus · Accepted Answer

To graph the equation $y=2+3x$, we plot the $y$-intercept at $(0,2)$ and use the slope $\frac{3}{1}$ to plot another point by moving up $3$ units and right $1$ unit to get $(1,5)$. Connecting these two points with a solid line gives:

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To graph the inverse, we swap the $x$ and $y$ variables and solve for $y$:
$$x = 2+3y \implies y = \frac{x-2}{3}$$
This gives us the equation for the inverse relation. To graph it, we plot the points that we used to graph the original relation, but in reverse order $(2,0)$ and $(5,1)$ (since the roles of $x$ and $y$ have been swapped). Connecting these two points with a dashed line gives:

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Note that the inverse relation is a reflection of the original relation over the line $y=x$, which is why we use a dashed line to indicate that it is not a function.

Graph the Equation of the Relation Using a Solid Line y=2+3xy = 2 + 3 xy=2+3x

Graph the Equation of the Relation Using a Solid Line $y = 2 + 3 x$