Cole Byrd
05/21/2024 · Elementary School
The function \( h \) is defined by \( h(x)=4 x+28 \). The graph of \( y=h(x) \) in the \( x y \)-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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Step-by-step Solution
To find the x-intercept, we set \( y = 0 \) and solve for \( x \):
\[ 0 = 4x + 28 \]
Subtract 28 from both sides:
\[ -28 = 4x \]
Divide both sides by 4:
\[ x = -7 \]
So the x-intercept is at \( (a, 0) \), where \( a = -7 \).
To find the y-intercept, we set \( x = 0 \) and solve for \( y \):
\[ y = 4(0) + 28 \]
\[ y = 28 \]
So the y-intercept is at \( (0, b) \), where \( b = 28 \).
Now we can find the value of \( a + b \):
\[ a + b = -7 + 28 \]
\[ a + b = 21 \]
The value of \( a + b \) is 21.
Quick Answer
The value of \( a + b \) is 21.
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