Question

Find the equation of the straight line passing through the point (0, -1)

which is perpendicular to the line
y=-3/4x-3

Answer 1

Explanation:

The given equation of the line is y = (-3/4)x - 3.

To find the equation of a line perpendicular to this line, we need to determine its slope first.

The slope of the given line is -3/4.

Since the line we are looking for is perpendicular, its slope will be the negative reciprocal of -3/4, which is 4/3.

So the slope of the line passing through (0, -1) and perpendicular to the given line is 4/3.

Using the point-slope form of the equation of a line, we can write:

y - y1 = m(x - x1)

where m is the slope and (x1, y1) is the given point.

Substituting the values we have, we get:

y - (-1) = (4/3)(x - 0)

Simplifying, we get:

y + 1 = (4/3)x

Subtracting 1 from both sides, we get:

y = (4/3)x - 1

Therefore, the equation of the straight line passing through the point (0, -1) and perpendicular to the line y = (-3/4)x - 3 is y = (4/3)x - 1.

Answer 2

y = (4/3)x - 1.

Explanation:

we have

y=-3/4x-3

comparing it with y=mx+c

where m is the slope and is c the y-intercept.

we get

slope (m) = -3/4.

Any line perpendicular to it will have a slope that is the negative reciprocal of -3/4, which is 4/3.

Let's call the equation of the line we're trying to find y = mx + b, where m is the slope and b is the y-intercept.

We know that the line passes through the point (0, -1), so we can substitute these values into the equation to get:

-1 = (4/3)(0) + b

Simplifying this, we get:

-1 = b

So the y-intercept of our line is -1.

Now we can substitute the slope and y-intercept into the equation to get:

y = (4/3)x - 1

Therefore, the equation of the straight line passing through the point (0, -1) which is perpendicular to the line y=-3/4x-3 is y = (4/3)x - 1.