Let's evaluate each statement regarding the linear equation \( y = 35x + 47 \).
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The slope of the line is 47: This statement is false. The slope (m) is the coefficient of \( x \), which is 35.
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The equation \( 35x − y = 47 \) is equivalent to the given equation.: To check this, we can rearrange: \( 35x - y = 47 \) can be rewritten as: \( y = 35x - 47 \), which is not equivalent to \( y = 35x + 47 \). This statement is false.
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The y-intercept for the line is 35: This statement is false. The y-intercept (b) is the constant term in the equation when it's in slope-intercept form \( y = mx + b \). Here, \( b = 47 \).
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The y-intercept for the line is 47: This statement is true. The y-intercept is indeed 47.
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The equation \( -35x + y = 47 \) is equivalent to the given equation.: To check this, we can rearrange: \( -35x + y = 47 \) can be rewritten as: \( y = 35x + 47 \), which is equivalent to the given equation. This statement is true.
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The slope of the line is 35: This statement is true. The slope of the line is indeed 35.
In summary, the true statements are:
- The y-intercept for the line is 47.
- The equation \( -35x + y = 47 \) is equivalent to the given equation.
- The slope of the line is 35.