Let's evaluate the statements one by one based on the given linear equation \( y = 35x + 47 \).
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The y-intercept for the line is 35.
False. The y-intercept is the value of \( y \) when \( x = 0 \). In this equation, substituting \( x = 0 \) gives \( y = 47 \). So, the y-intercept is 47, not 35. -
The equation \(-35x + y = 47\) is equivalent to the given equation.
False. To check this, we can rearrange \(-35x + y = 47\). Adding \(35x\) to both sides gives \(y = 35x + 47\), which is the original equation. Thus, the statement is true as it is equivalent. -
The y-intercept for the line is 47.
True. As derived earlier, the y-intercept when \( x = 0 \) is indeed \( y = 47 \). -
The slope of the line is 47.
False. The slope of the line is the coefficient of \( x \) in the standard form \( y = mx + b \), where \( m \) is the slope. Here, the slope is 35, not 47. -
The equation \( 35x - y = 47 \) is equivalent to the given equation.
True. We can rearrange \( 35x - y = 47 \) by isolating \( y \) to get \( y = 35x - 47 \). This is not the same as the original equation, so the statement is false. -
The slope of the line is 35.
True. The slope of the line (\( m \)) from the equation \( y = 35x + 47 \) is indeed 35.
Summary of True Statements:
- The equation \(-35x + y = 47\) is equivalent to the given equation. (True)
- The y-intercept for the line is 47. (True)
- The slope of the line is 35. (True)
Final Selections:
- The equation \(-35x + y = 47\) is equivalent to the given equation.
- The y-intercept for the line is 47.
- The slope of the line is 35.
1 answer