Comparing Gradient: Highest & Lowest, Vector/Scalar?

[songoku]

If, let say, I have 3 equation of lines:
Line 1: y = 3x + 10
Line 2: y = 0
Line 3: y = -4x

which line has the highest and lowest gradient?

Is gradient in equation of line vector quantity or scalar quantity?

Do we say gradient = 0 is higher than gradient = -4 or is gradient = -4 is higher than 0 because the gradient is only "directed" downwards?

Thanks

 

[andrewkirk]

Usually it would be regarded as a vector quantity, so that Line 1 has the highest gradient.
A term that is sometimes used for gradient as a scalar is 'steep'. We would say the Line 3 has the steepest gradient.

If it is an assignment question and you are not sure what the lecturer intended, I suggest you give both answers and explain why they are different.

 

[Mark44]

The three equations are those of lines. The terminology we use in the US is "slope," as "gradient" is usually reserved to the discussion multivariate functions.
For example, if $w = f(x, y, z)$ is a function of three variables, the gradient of f, denoted $\nabla f$ can be written as $\nabla f = \frac{\partial f}{\partial x} \textbf i + \frac{\partial f}{\partial y}\textbf j + \frac{\partial f}{\partial z} \textbf k$.

The slopes of the three lines are 3, 0, and -4, respectively. Although -4 < 0 < 3, the third line is the steepest.

 

[songoku]

Usually it would be regarded as a vector quantity, so that Line 1 has the highest gradient.
A term that is sometimes used for gradient as a scalar is 'steep'. We would say the Line 3 has the steepest gradient.

Is there difference between "highest gradient" and "steepest gradient"?
If I want to find highest gradient, it is line 1 but if I want to find steepest gradient, it is line 3?

If it is an assignment question and you are not sure what the lecturer intended, I suggest you give both answers and explain why they are different.

I need to draw something related to gradient (slope) so I have to understand about this

Thanks