Question

Write an equation of the line that is perpendicular to y=-2/7x+9 and that passes through (4,-6)

i would like to know the answer to this problem please and thank you. if anyone knows please let me know id appreciat

Answer 1

y =
`(7)/(2)` x - 20

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

given the equation

y = -
`(2)/(7)` x + 9 ← in slope- intercept form

with slope m = -
`(2)/(7\\)`

given a line with slope m then the slope of a line perpendicular to it is

`m_(perpendicular)` = -
`(1)/(m)` = -
`(1)/(-(2)/(7) )` =
`(7)/(2)` , then

y =
`(7)/(2)` x + c ← is the partial equation

to find c , substitute (4, - 6 ) for x and y into the partial equation

- 6 =
`(7)/(2)` (4) + c = 14 + c ( subtract 14 from both sides )

- 20 = c

y =
`(7)/(2)` x - 20 ← equation of perpendicular line

Answer 2

The equation of the line that is perpendicular to y = -2/7x + 9 and passes through the point (4, -6) is y = (7/2)x - 20.

Step-by-step explanation:

To find the equation of a line that is perpendicular to another line, we need the negative reciprocal of the original line's slope. The given line has an equation y = -2/7x + 9, which means its slope (m) is -2/7. The negative reciprocal of -2/7 is 7/2. This will be the slope of the perpendicular line.

Next, we use the point-slope form of a line's equation, which is y - y1 = m(x - x1), where (x1, y1) is a point on the line, and m is the slope of the line. Substituting the point (4, -6) and the slope 7/2, we get:

y + 6 = (7/2)(x - 4)

To find the slope-intercept form, solve for y:

y + 6 = (7/2)x - 14

y = (7/2)x - 14 - 6

y = (7/2)x - 20

The equation of the line perpendicular to the original line and passing through the point (4, -6) is y = (7/2)x - 20.