The equation of line l is y = 3x/a+ 5, where a is a positive constant. If the value of a in this equation is doubled, then the resulting equation will represent a line whose slope is how many × the slope of line l?
The resulting equation will represent a line whose slope is 1/2 the slope of line l.
The given equation of line l is in the form y = mx + b, where m represents the slope. In this case, the slope is 3/a. When the value of a is doubled, the new slope becomes 3/(2a), which simplifies to (3/2) * (1/a). Thus, the slope of the new line is half of the original slope.
If the slope were doubled, it would require that the expression for the slope becomes 2 * (3/a). However, when a is doubled, the slope decreases instead of increasing, making this choice incorrect.
This choice suggests that the new slope is 3/2 times the original slope. However, upon doubling a, the new slope becomes (3/2) * (1/a), indicating a reduction rather than an increase. Hence, this option does not hold true.
When a is doubled, the new slope becomes 3/(2a), which can be simplified to (1/2) * (3/a). This shows that the new slope is indeed 1/2 the original slope, confirming this as the correct choice.
For the new slope to equal 3/10, the relationship between the original slope and the new slope would need to be established. However, since the original slope is 3/a, and the new slope is halved when a is doubled, this specific value does not reflect the correct ratio. Thus, this option is incorrect.
The relationship between the slopes of the lines illustrates that doubling the positive constant a results in a new slope that is half the original slope of line l. Therefore, the answer indicates that the slope of the resulting line is 1/2 the slope of the original line, demonstrating how alterations in constants directly influence linear equations.
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