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The function $h$ is defined by $h(x)=4x+28$. The graph of $y=h(x)$ in the $xy$-plane has an $x$-intercept at $(a,0)$ and a $y$-intercept at $(0,b)$, where $a$ and $b$ are constants. What is the value of $a+b$?

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The function $h$ is defined by $h(x)=4x+28$. The graph of $y=h(x)$ in the $xy$-plane has an $x$-intercept at $(a,0)$ and a $y$-intercept at $(0,b)$, where $a$ and $b$ are constants. What is the value of $a+b$?

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Choice A is correct. The $x$-intercept of a graph in the $xy$-plane is the point on the graph where $y=0$. It's given that function $h$ is defined by $h(x)=4x+28$. Therefore, the equation representing the graph of $y=h(x)$ is $y=4x+28$. Substituting $0$ for $y$ in the equation $y=4x+28$ yields $0=4x+28$. Subtracting $28$ from both sides of this equation yields $-28=4x$. Dividing both sides of this equation by $4$ yields $-7=x$. Therefore, the $x$-intercept of the graph of $y=h(x)$ in the $xy$-plane is $(-7,0)$. It's given that the $x$-intercept of the graph of $y=h(x)$ is $(a,0)$. Therefore, $a=-7$. The $y$-intercept of a graph in the $xy$-plane is the point on the graph where $x=0$. Substituting $0$ for $x$ in the equation $y=4x+28$ yields $y=4(0)+28$, or $y=28$. Therefore, the $y$-intercept of the graph of $y=h(x)$ in the $xy$-plane is $(0,28)$. It's given that the $y$-intercept of the graph of $y=h(x)$ is $(0,b)$. Therefore, $b=28$ If $a=-7$ and $b=28$, then the value of $a+b$ is $-7+28$, or $21$.

Choice B is incorrect. This is the value of $b$, not $a+b$.

Choice C is incorrect and may result from conceptual or calculation errors.

Choice D is incorrect. This is the value of $-a+b$, not $a+b$.

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The function $h$ is defined by $h(x)=4x+28$. The graph of $y=h(x)$ in the $xy$-plane has an $x$-intercept at $(a,0)$ and a $y$-intercept at $(0,b)$, where $a$ and $b$ are constants. What is the value of $a+b$?

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