Question

Write an equation of the line that passes through (-4, 2) and is perpendicular to the line y = 2/7x-8.

An equation of the perpendicular line is y=

Answer 1

Answer: y=-7/2x-12

Step by step:

The line y = 2/7x-8 is in slope-intercept form y=mx+ b

m=slope=2/7

In order to find a line that is perpendicular, you need to "flip it" then take the opposite sign so for our perpendicular line the slope is:

m
`-(7)/(2)` and passes through (-4,2) Now you need to use slope-point form

(y - y1)=m(x - x1)

(y - 2) = -7/2 (x + 4) now simplify to look like y=mx + b

`y-2=-(7)/(2)x-14 )\\\\y=-(7)/(2)x -12`

Answer 2

To find the equation of a line that is perpendicular to y = (2/7)x - 8, we first need to determine the slope of the original line.

The slope of y = (2/7)x - 8 is 2/7, because the equation is in slope-intercept form (y = mx + b), where m is the slope.

Since we want the new line to be perpendicular to this line, we know that its slope will be the negative reciprocal of 2/7.

To find the negative reciprocal, we flip the fraction and change the sign:

-2/7

Now we have the slope of the new line.

Next, we use the point-slope form of the equation of a line to write the equation, using the point (-4, 2) and the slope -2/7:

y - y1 = m(x - x1)

where x1 = -4, y1 = 2, and m = -2/7.

Plugging in the values, we get:

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

Simplifying:

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

Multiplying both sides by 7 to eliminate the fraction:

7y - 14 = -2(x + 4)

Distributing the -2:

7y - 14 = -2x - 8

Adding 2x and 14 to both sides:

2x + 7y = 6

Therefore, the equation of the line that passes through (-4, 2) and is perpendicular to y = (2/7)x - 8 is 2x + 7y = 6.