The gradient of the code equals delta Y over delta X, right.

斜率等于△y/△x，好。

The students could then measure the slope.

后，学生们可以测量斜率。

Just like we study slope independently of other factors.

就像我们独立于其他因素研究斜率一样。

So a little bit less than a slope of one.

所以比一个斜率小一点。

So our regression slope is a little bit less than 1.

所以我们的回归斜率略小于 1。

If that's true, then the slopes of their diagonal sides should be the same.

如果那是真的，那么它们的对角线边的斜率应该相同。

For a lesson about slope, or direction of a line in algebra, the chatbot suggested students build ramps out of cardboard.

在一堂关于斜率（即线性代数）的课上，聊天机器人建议学生们用纸板搭建斜坡。

And that factor is angular momentum.

斜率，那个因素就是角动量。

And then we're going to have a slope a little bit less than 1.

后我们将有一个略小于 1 的斜率。

The angle between the force of gravity and the component pointing into the ramp is called theta.

重力与元素之间的角度 斜率内的向量称为 theta。

The slope at that point in that direction will also be 0, and that is our minimum point.

该点在该方向的斜率也将为 0，这就是我们的最小点。

In other words: if down the ramp is the positive direction, is the net force positive or zero?

阻性辅音，换句话说：如果方向 在正斜率下，全力为 0 吗？

The triangle soldier's diagonal, however, goes up 3 and over 8, making its slope three eights, or 0.375.

而，三角形士兵的对角线上升 3 并超过 8，使其斜率变为八分之三，即 0.375。

The trapezoid soldier's diagonal side goes up 2 and over 5, giving it a slope of two fifths, or 0.4.

梯形士兵的对角线边上升 2 并超过 5，斜率为五分之二，即 0.4。

This is the slope on the line, and this is the y-intercept.

这是直线的斜率，这是 y 轴截距。

So we can literally find the slope of that line and then the the y intercept, the b there.

所以我们可以从字面上找到那条线的斜率，后是 y 截距，b 在那里。

But when she calculates these slopes using the tried and true formula " rise over run, " a most curious thing happens.

但是，当她使用久经考验的真实公式“上升超过运行”计算这些斜率时，一件最奇怪的事情发生。

So when x is equal to negative 2, the y value on the line is going to be the slope.

所以当 x 等于负 2 时，直线上的 y 值将成为斜率。

That right there is the slope of our regression line.

右边是我们回归线的斜率。

So the slope in this direction, that's the partial derivative with respect to m, is going to be flat.

所以这个方向的斜率，即关于 m 的偏导数， 将是平坦的。