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Predict which of the following linear functions would have a graph with the steepest, most vertical, slope.(1 point)

Responses

y=2x+5
y is equal to 2 x plus 5

y=3x+4
y is equal to 3 x plus 4

y=−5x
y is equal to negative 5 x

y=−4x+8

1 answer

To determine which of the given linear functions has the steepest slope, we can look at the coefficients of \( x \) in each function:

  1. \( y = 2x + 5 \) has a slope of \( 2 \).
  2. \( y = 3x + 4 \) has a slope of \( 3 \).
  3. \( y = -5x \) has a slope of \( -5 \).
  4. \( y = -4x + 8 \) has a slope of \( -4 \).

The steepness of a slope can be quantified by the absolute value of the slope. Therefore, we evaluate the absolute values of the slopes:

  1. \( |2| = 2 \)
  2. \( |3| = 3 \)
  3. \( |-5| = 5 \)
  4. \( |-4| = 4 \)

The slope with the largest absolute value is \( -5 \) in the function \( y = -5x \).

Thus, the graph with the steepest, most vertical slope is:

\( y = -5x \).