Question

Name cach line in the figure whose slope is:

a. positive

b. negative

c. zero

d. not defined

Short answer

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

Step-by-step solution

a.Step-1 – Given

The given figure is:

Step-2 – To determine

We have tofind 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 tofind 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 linek has negative slope.

c.Step-1 – Given

The given figure is:

Step-2 – To determine

We have tofind 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 tofind 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.