Question

Write the point-slope form of the line that passes through (5, 5) and is perpendicular to a line with a slope of 1/4. Include all of your work in your final answer. Type your answer in the box provided or use the upload option to submit your solution.

Answer 1

The point-slope form of the line perpendicular to a line with a slope of 1/4 and passing through (5, 5) is y - 5 = -4(x - 5).

Step-by-step explanation:

To write the point-slope form of a line that is perpendicular to another line, we need to find the perpendicular slope. Since the given slope of the original line is 1/4, the perpendicular slope is the negative reciprocal of 1/4, which is -4 (since the product of the slopes of two perpendicular lines in a plane is -1).

Next, we use the point-slope form, which is y - y1 = m(x - x1), where m is the slope of the line and (x1, y1) is a point on the line. Plugging in the slope -4 and the point (5, 5), we get:

y - 5 = -4(x - 5)

This is the equation of the line in point-slope form.

Answer 2

ur given a slope of 1/4. A perpendicular line will have a negative reciprocal slope. All that means is " flip " the slope and change the sign. So our perpendicular line will need a slope of -4. (see how I flipped 1/4 and made it 4/1 or just 4, and then changed the sign making it -4)

y - y1 = m(x - x1)
slope(m) = -4
(5,5)...x1 = 5 and y1 = 5
now we sub
y - 5 = -4(x - 5) <== ur perpendicular equation in point-slope form