Question

pls help!! What is an equation of the line that passes through the point (8,−8) and is perpendicular to the line 4x−3y=18?

Answer 1

y = (-3/4)x - 2

Explanation:

To find the equation of the line that passes through the point (8,-8) and is perpendicular to the line 4x-3y=18, we need to use the fact that the slopes of two perpendicular lines are negative reciprocals of each other.

First, let's rewrite the equation 4x-3y=18 in slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept:

4x - 3y = 18

-3y = -4x + 18

y = (4/3)x - 6

So the slope of the given line is 4/3.

The slope of the line perpendicular to the given line is the negative reciprocal of 4/3, which is -3/4.

Now we can use the point-slope form of the equation of a line:

y - y1 = m(x - x1),

where (x1,y1) is the given point and m is the slope we just found.

Plugging in the values, we get:

y - (-8) = (-3/4)(x - 8)

Simplifying:

y + 8 = (-3/4)x + 6

y = (-3/4)x - 2

So the equation of the line that passes through the point (8,-8) and is perpendicular to the line 4x-3y=18 is y = (-3/4)x - 2

Answer 2

y =
`(-3)/(4)` x - 2

Explanation:

4x - 3y = 18 Convert to the slope intercept form of the line

4x - 4x - 3y = -4x + 18 Subtract -x from both sides

-3y = -4x + 18 Divide all the way though by -3

`(-3y)/(-3)` =
`(-4x)/(-3)` +
`(18)/(-3)`

y =
`(4)/(3)` x -6

The slope of this equation is
`(4)/(3)`, so the perpendicular slope would be
`(-3)/(4)`. Use this slope and the point (8, -8) to find the y-intercept.

-8 =
`(-3)/(4)`(8) +b

-8 = -6 +b Add 6 to both sides

-2 = b

Y= mx + b

y = _x + _ Put in the blanks what we found for m (slope) and b (y-intercept)

y =
`(-3)/(4)` x - 2

Helping in the name of Jesus.