Question

page 14 of 14
Changing Slope and y-intercept Quick Check
2 of 52 of 5 Items
Question
Predict which of the following linear functions would have a graph with the steepest, most vertical, slope.(1 point)
Responses

y=−4x+8
y is equal to negative 4 x plus 8

y=−5x
y is equal to negative 5 x

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

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

Answer 1

To determine which linear function has the steepest, most vertical slope, we need to examine the slopes of each of the given equations. The slope is the coefficient of \(x\) in each equation.

The given functions are:

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

Now, we can compare the absolute values of the slopes, because a steeper slope will have a larger absolute value:

- For \(y = -4x + 8\), the slope is \(-4\) (absolute value: 4).
- For \(y = -5x\), the slope is \(-5\) (absolute value: 5).
- For \(y = 3x + 4\), the slope is \(3\) (absolute value: 3).
- For \(y = 2x + 5\), the slope is \(2\) (absolute value: 2).

The largest absolute value of the slopes is 5, which corresponds to the function \(y = -5x\).

Therefore, the linear function with the steepest, most vertical slope is:

**\(y = -5x\)**.