Q. 1 - Geometry

Question

Name cach line in the figure whose slope is:

a. positive

b. negative

c. zero

d. not defined

Step-by-Step Solution

Answer

1. The lines $n\text{ and }y$ have positive slope.
2. The slope of $y-\text{axis}$ is undefined.

a. Step-1 – Given

The given figure is:

Step-2 – To determine

We have to find the lines with positive slope.

Step-3 – Calculation

We know that the slope is the ratio of the y-intercept to the x-intercept of a line.

$\text{slope}=\frac{y-\text{intercept}}{x-\text{intercept}}$

From the given figure, we have that $y-\text{intercept}$ and $x-\text{intercept}$ of lines are positive. 

So, the lines $n\text{ and }y$ have positive slopes.

b. Step-1 – Given

The given figure is:

Step-2 – To determine

We have to find the lines with negative slope.

Step-3 – Calculation

We know that the slope is the ratio of the y-intercept to the x-intercept of a line.

$\text{slope}=\frac{y-\text{intercept}}{x-\text{intercept}}$

From the given figure, we have that $y-\text{intercept}$ of the line k is positive and the $x-\text{intercept}$ is negative.

So, the line k has negative slope.

c. Step-1 – Given

The given figure is:

Step-2 – To determine

We have to find the lines with zero slope.

Step-3 – Calculation

From the given figure, we see that the line l is making an angle of $0^{°}$with the $x-\text{axis}$.

It means $\text{slope}=\tan \theta =\tan 0^{°}=0$.

So, the slope of line l is zero.

 

d. Step-1 – Given

The given figure is:

Step-2 – To determine

We have to find the lines with undefined slope.

Step-3 – Calculation

From the given figure, we see that the line X is making an angle of ${90}^{°}$in the anticlockwise direction with the positive $x-\text{axis}$.

So, the slope of line X is undefined.