Mathematics, 13.07.2019 19:00 bigwaYne

Write an equation of a line in slope intercept form that is parallel to the line x + 4y = 6 and passes through (-8, 5). show work. write an equation of a line in slope intercept form that is perpendicular to the line 2x -3y = 12 and passes through the point (2, 6). show work.

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Answer from: Laydax1587

Let us find the slope of the line : x+ 4y = 6

we can write it as 4y = -x +6

y = -(1/4) x + ( 6/4)

slope of the line y= mx + b is m

so here slope = m = -1/4

because we have to find a paraller line so the slope for required line would be same : -1/4

equation of the line having slope m and passing through x1 y1 is :

Y= m( X-x1) + y1

let's plug m= -1/4 x1= -8 and y1 = 5

Y= (-1/4) ( X- -8) + 5

Y= ( -1/4) ( x+8) + 5

Y= (-1/4)( X ) + (-1/4)( 8) + 5

Y= (-1/4) x + 3

Let us now work on second part :

given line is : 2x- 3y = 12

let's write it -3y = -2x +12

y= (-2/-3) x + ( 12/ -3)

Y= ( 2/3) x - 4

slope of this line is 2/3

the required line is perpendicular to it

so the slope of required line = negative resiprocal of this slope =

(-1/ slope of this line ) = -1/( 2/3) = -3/2

Equation of line with slope m= -3/2 and passing through x1= 2 and y1 = 6 is :

Y= m( X-x1) + y1

Y= ( -3/2) ( X- 2) + 6

Y= (-3/2) X - 2(-3/2) + 6

Y= ( -3/2 ) X + 9

Answer : for part 1 : Y= ( 2/3) x - 4

Answer for part 2 : Y= ( -3/2 ) X + 9

Answer from: wednesdayA

The slope of the line x+4y=6 is $m=-\frac{1}{4}$ .

The equation of the line in slope intercept form parallel to x+4y=6 is

$y=-\frac{1}{4} x+c$

Since the above line passes through (-8,5) is

$5=-\frac{1}{4} (-8)+c \\ c=3$

Thus the equation of the line in slope intercept form is $y=-\frac{1}{4} x+3$

The slope of the line 2 x-3y=12 is $m=\frac{2}{3}$ .

The line perpendicular to the above line has slope $-\frac{1}{m} =-\frac{3}{2}$

Its equation is $y=-\frac{3}{2} x+c$ . Since this line passes through, (2,6) ,

$6=-\frac{3}{2} (2)+c\\c=9$ .

Thus the equation of the line in slope intercept form is $y=-\frac{3}{2} x+9$

Answer from: Quest

first anwser choice.

step-by-step explanation:

the greater/less or equal to symbol (> or < with the line at the bottom) is a closed/filled in circle.

when multiplying or dividing by a negative on both sides you have to flip the inequality sign. this rule only applies to multiplying or dividing by a negative number in inequality equations. this rule is really important.

-5c + 2 _< _27

subtract from both sides by 2

-5c _< _ 27

divide both sides by -5

c _< _ 5.4

flip the inequality sign

c _> _5.4

the only possible answer that would match the simplified inequality is the first answer choice

5c+2< 27 i really do not understand this.

Answer from: Quest

The distance from point a to point c across the coordinate plane is aproxamatly 8.94 rounded to the nearest hundredth. you use a^2 + b^2 =c^2
Apply the pythagorean theorem to find the distance between points a and c