Question

Write the equation of a line that is perpendicular to x = 3 and that passes through the point ( 0 , − 4 )

Answer 1

We have to write the equation of a line that is perpendicular to the line $x=3$ and that passes through the point $(0,-4)$.

The general equation of a line in the slope-intercept form is given by:

$y=mx+b$

Where, 'm' is the slope and 'b' is the y-intercept.

Now, we need to find the slope first,

The required line is perpendicular to the line $x=3$. Slope of the line $x=3$ is undefined. A line perpendicular to that must have slope of '0'. That implies, our required line is parallel to the x-axis.

Therefore, m=0

Now that line is passing through the point $(0, -4)$.

We can plug in the points to the find the value of y-intercept. After plugging the values, we get:

$y=0 \times 0+(-4)=-4$

Hence, the equation of the required line is $y=-4$.