# Which of the following is the equation of a line (in point slope form) that is perpendicular to y=-1/4+3 and passes through the point (-3,2)?

###### Question:

## Answers

[tex]m_1 = 6, m_2 = 5[/tex]In general, the functions are of the form

[tex]y = f(x) = mx +b[/tex]

The linear functions are

[tex]f(x) = 6x + 4\\f(x) = 5x -2[/tex]

Let [tex]m_1 = 6, m_2 = 5[/tex].

A. False: the lines are parallel if [tex]m_1 = m_2[/tex] but this does not happen.

B. False. The lines are perpendicular if [tex]m_1m_2 = -1[/tex] and clearly this does not happen.

C. [tex]6x + 4 = 5x - 2\\x = -6\\6(-6) + 4 = -32 = 5(-6) -2[/tex]

Then C is true.

D. False. The lines are not the same.

A.

[tex]y - 5 = -2(x-6)[/tex]

Negative reciprocal gives you the perpendicular slope so negative reciprocal of 1/2 is -2.

Then apply point-slope form.

B. The answer is x = 6.

The midpoint of JK is

[tex]\left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) = \left( \frac{8+ 4}{2}, \frac{4 + 4}{2} \right) = \left(6,4\right)[/tex]

The line that goes through JK is just a horizontal line [tex]y = 4[/tex] because the y-coordinate does not change. So its perpendicular bisector is the vertical line that goes through the x-coordinate of the midpoint, that is, [tex]x = 6[/tex].

Q1 5:3

Step-by-step explanation:

500 / 100 = 5

300 / 100 = 3

500:300 simplified to 5:3

y = 1/4x + 17/4

Step-by-step explanation:

Slope-Intercept Form: y = mx + b

Perpendicular lines have the negative reciprocal slope.

m = 1/4

y = 1/4x + b

4 = 1/4(-1) + b

4 = -1/4 + b

17/4 = b

y = 1/4x + 17/4

You do not have any points to right the point slope form.

Step-by-step explanation:

Bjhgggfsdfthh by

Point slope form is [tex]y-y1=m(x-x1)[/tex]

Since we have to write the equation of a perpendicular line we will have to use the slope that is opposite and reciprocal.

[tex]y - (-1) = - \frac{1}{5} (x - (-2))[/tex]

[tex]y + 1 = - \frac{1}{5} (x + 2)[/tex]

Hope this helps :)

y-9 = -1/12(x-8)

Step-by-step explanation:

To write an equation of a line perpendicular to the graph of y = 12x-3 and passing through the point, we will follow the following steps.

The standard form of point-slope form of the equation of a line is given as

y − y1 = m(x − x1),

m is the slope of the unknown line

(x1, y1) is a point on the line.

Step 1: We need to calculate the slope of the known line first,

Given y = 12x-3

from the equation, m = 12 on comparison.

Step 2: get the slope of the unknown line. since the line given is perpendicular to the line y = 12x - 3, the product of their slope will be -1 i.e Mm = -1

M = -1/m

M is the slope of the unknown line

M = -1/12

Step 3: We will substitute M = -1/12 and the point (8, 9) into the point-slope form of the equation of a line i.e y − y1 = M(x − x1),

M = -1/12, x1 = 8 and y1 = 9

y-9 = -1/12(x-8)

The answer would be c

answer: it's d

step-by-step explanation: