Question

find the equation of the line passing through the point (0,2) why is perpendicular to the line y=1/4x+5

Answer 1

To find the equation of a line passing through the point (0,2) that is perpendicular to the line y = 1/4x + 5, we can use the following steps:

1. Find the slope of the given line y = 1/4x + 5. Since this line is in slope-intercept form (y = mx + b), we can see that the slope of the line is 1/4.
2. Find the slope of the line that is perpendicular to the given line. The slopes of two perpendicular lines are negative reciprocals of each other. So, the slope of the new line is the negative reciprocal of 1/4, which is -4.
3. Use the point-slope form of the equation of a line to write the equation of the new line. We can use the point (0,2) and the slope -4 in the point-slope form:

y - y1 = m(x - x1)

where (x1, y1) is the given point and m is the slope of the line. Substituting the values, we get:

y - 2 = -4(x - 0)

Simplifying, we get:

y - 2 = -4x

Adding 2 to both sides, we get the final equation:

y = -4x + 2

So, the equation of the line passing through the point (0,2) and perpendicular to the line y = 1/4x + 5 is y = -4x + 2.

Answer 2

Answer: y=-4x+c

Step-by-step explanation: Let's start off with the gradient of the line:

The gradient of such a line would be —1/(1/4) = -4, as it's the negative reciprocal of the gradient of the line it's perpendicular to.

So now you've got some line in the form of:

y = -4x + c

The line passes through (0,2), so chuck these numbers in and you get a value of 2 for c. If you're sharp, you might spot that this point is the y-intercept of the line since the x- coordinate is 0, this point is on the Y-axis, and you don't even have to throw numbers in.

Therefore the equation of the line is:

y = -4x + 2