Question

Can someone help me with this math homework please!

Answer 1

1: gets steeper

2: gets less steep

3: negative

Explanation:

"As the value of m changes from 1 to 3, the graph gets steeper."

m is the slope of the line, and when it increases, there's more "rising" then "running", so it becomes more steep.

"As the value of m changes from -6 to -1, the graph gets less steep."

When the value of m increases, it gets more steep. It makes sense since -6 is less than -1. However, in this scenario, the negative sign doesn't "affect" the slope of the graph. It just flips the graph over the y-axis.

So you have to think of it as if the negative signs were gone and it was 6 to 1.

In that case, the slope is decreasing, so it's getting less steeper.

"If the value of m is negative, the slope of the line is negative."

The m variable represents the slope in slope-intercept form, so if m is negative, that's the same as saying the slope is negative.

Hope this helps (●'◡'●)

Answer 2

Answers:

1. gets steeper
2. gets less steep
3. negative

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Explanations:

1. We have m = 1 change to m = 3. As we get further away from 0, the slope gets steeper.
2. Now we're going from m = -6 to m = -1, and we're getting closer to zero. So we're going in the opposite direction as problem 1. Therefore, the line is getting more shallow or less steep.
3. Negative values of m correspond directly to negative slopes, and vice versa. This is simply because m is the slope. Negative slopes visually show a line that goes downhill when you move to the right.