Chapter 3, Problem 1RVS

To determine

The correct graph for the equation $y=x+4$.

Answer to Problem 1RVS

Solution:

The correct matching graph for the equation $y=x+4$ is (C).

Explanation of Solution

Given Information:

There is an equation is given as $y=x+4$.

The given options to choose the graphs are,

(A)

(B)

(C)

(D)

(E)

(F)

(G)

(H)

(I)

(J)

Consider the given equation $y=x+4$.

As the equation is in the form $y=mx+c$, so the given equation is a straight line. To identify its exact location, find the $x$ and $y$ intercept.

For $x$ intercept in the equation $y=x+4$, put the value of $y=0$,

$\begin{array}{c}y=x+4\\ 0=x+4\\ -4=x\end{array}$

Thus, the required line passes through $\left(-4,0\right)$.

For $y$ intercept in the equation $y=x+4$, put the value of $x=0$,

$\begin{array}{c}y=x+4\\ y=0+4\\ y=4\end{array}$

Thus, the required line also passes through $\left(0,4\right)$.

There is only one line, which is passes through $\left(-4,0\right)$, and $\left(0,4\right)$ both.

Therefore, the correct matching option is (C).