Question

Part A: What is the equation of the line that is perpendicular to the line y=-1/4x+5 and passing through the point (2,-1)? Write your equation in the point slope form. Part B. Does the point (3,3) lie on the line you wrote an equation for Part A? Justify your awnser?

Answer 1

Part A:

To find the equation of a line that is perpendicular to another line, we need to know that the slopes of the two lines are negative reciprocals of each other. The given line has a slope of -1/4, so the slope of the perpendicular line will be 4.

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

y - (-1) = 4(x - 2)

Simplifying this equation, we get:

y + 1 = 4x - 8

y = 4x - 9

Therefore, the equation of the line that is perpendicular to the line y=-1/4x+5 and passing through the point (2,-1) is y=4x-9, written in point-slope form.

Part B:

To check if the point (3,3) lies on the line y=4x-9, we can substitute x=3 and y=3 into the equation and see if it is a true statement:

y = 4x - 9

3 = 4(3) - 9

3 = 3

This is not a true statement, since 3 does not equal 0. Therefore, the point (3,3) does not lie on the line y=4x-9.

Answer 2

Part A:The given line has a slope of -1/4. Therefore, the slope of the line perpendicular to it would be the negative reciprocal of -1/4, which is 4.We know that the line passes through the point (2,-1). We can use the point-slope form of the equation to find the equation of the line:y - (-1) = 4(x - 2)

y + 1 = 4x - 8

y = 4x - 9So the equation of the line that is perpendicular to y=-1/4x+5 and passing through the point (2,-1) is y = 4x - 9 in point-slope form.Part B:To determine if the point (3,3) lies on the line, we can substitute x = 3 and y = 3 into the equation we found in Part A:y = 4x - 9

3 = 4(3) - 9

3 = 3Since the equation is true, the point (3,3) lies on the line y = 4x - 9.