Question

Find the equation of the line parallel to x-axis and having intercept -2 on y-axis.
a) $x=2$
b) $x=-2$
c) $y=2$
d) $y=-2$

Answer 1

Hint: Here, first write the equation of a straight line passing through a point (0, c) on y-axis and parallel to x-axis. We will get the equation as $y=c$. Now, here the y-intercept is given as -2. Hence the point will be (0, -2). Now, write the equation of the line where c = -2.

Complete step-by-step answer:

Here, we are given that a line is parallel to x-axis and having intercept -2 on y-axis.

Now, we have to find the equation of the line parallel to x-axis and having intercept -2 on y-axis.

We know that if a straight line is passing through a point (0, c) on y-axis and parallel to x-axis,

then the equation of the straight line is $y=c$.

Here, it is given that the line is passing through (0, -2)

Now, by putting (0, -2) in $y=c$ we get:

$c=-2$

$\Rightarrow y=-2$

Therefore, we can say that the equation of the line is $y=-2$.

Hence, the correct answer for this question is option (d).

Note: In other ways, by the general equation of the straight line we can find the equation of the line. The general equation of a straight line is $y=mx+c$, where m is the slope and c is the y intercept. This equation is also known as slope-intercept form. Here the y intercept is given as -2 and the line is parallel to x-axis. Therefore, slope of the line, m = 0. Then the equation of the line is $y=-2$.