Question

Find the equation of the line that passes through the point (5, -4) and is perpendicular to the line y=1/4x - 2 .

Answer 1

y = -4x + 16

Explanation:

For questions like this, I would first find the slope of the line that we are trying to find the equation for. To do this, I would use the line y = 1/4x - 2 and find the slope of a line that would be perpendicular to it. Taking the negative reciprocal of the slope of y = 1/4x - 2 will do just that.

By looking at the equation y = 1/4x - 2, we can see that the slope of the line is 1/4. The negative reciprocal of 1/4 would be -4, which would be the slope of the line whose equation we are trying to find.

Since we have a point on the line, and we now have the slope of the line, we can now make an equation for the line in point-slope form:

y + 4 = -4(x - 5)

Now while this is an equation for the line, lets try to get it into slope-intercept form:

y + 4 = -4(x - 5)

Distribute the -4 on the right side of the equation.

y + 4 = -4x + 20

Subtract 4 from both sides.

y = -4x + 16

And now we have the equation of the line in slope-intercept form.

I hope you find my answer helpful.

Answer 2

The equation of the line is:

`y = -4\,x +16`

Explanation:

A line perpendicular to the given one is going to have a slope equal to the opposite of the reciprocal of 1/4. That is the slope of the new line will be "-4".

Now we write the point-slope form for a line using the info provided of slope -4 and point (5, -4):

`y-y_0=m\,(x-x_0)\\y - (-4) = -4 \,(x-5)\\y+4 = -4\,x +20\\y = -4\,x +16`