Chapter 7, Problem 1RVS

Use after Section 7.6.

Match each equation or inequality or system of equations or inequalities with its graph.

$x+y=3$

To determine

The right match for the equation $x+y=3$ with its graph from the given options.

Answer to Problem 1RVS

Solution:

The correct match for the equation $x+y=3$ is G.

Explanation of Solution

Given Information:

The provided equation is $x+y=3$ and the provided graphs are:

Consider the given equation that is $x+y=3$.

Thus, to graph the equation $x+y=3$. find the x and y intercept.

Now, substitute $x=0$ in the equation $x+y=3$.

$\begin{array}{c}x+y=3\\ 0+y=3\\ y=3\end{array}$

Thus, y intercept is $\left(0,3\right)$.

Substitute $y=0$ in the equation $x+y=3$.

$\begin{array}{c}x+y=3\\ x+0=3\\ x=3\end{array}$

Thus, x intercept is $\left(3,0\right)$.

The equation $x+y=3$ can be written in slope intercept form as,

$y=-x+3$

Hence, the slope of the equation is $-1$.

Now plot the graph of the equation $x+y=3$ by joining the points $\left(3,0\right)$, $\left(0,3\right)$ with slope $-1$.

Hence, the graph of the equation $x+y=3$ correct matches with option G.