Point-slope form of a line: we need a point (x₀,y₀) and the slope "m".
y-y₀=m(x-x₀)
slope intercept form :
y=m+b
m=slope
If the line is parallel to y=2/3 x-0, the line will have the same slope, therefore the slope will be: 2/3.
Data:
(8,4)
m=2/3
y-y₀=m(x-x₀)
y-4=2/3(x-8)
y-4=2/3 x-16/3
y=2/3 x-16/3+4
y=2/3 x-4/3 (slope intercept form)
Answer: The equation of the line would be: y=2/3 x-4/3.
if we have the next slope "m",then the perendicular slope will be:
m´=-1/m
We have this equation: y=2/3 x+0; the slope is: m=2/3.
The perpendicular slope will be: m`=-1/(2/3)=-3/2
And the equation of the perpendicular line to : y=2/3 x+0, given the point (8,4) will be:
y-y₀=m(x-x₀)
y-4=-3/2 (x-8)
y-4=-3/2 x+12
y=-3/2x + 12+4
y=-3/2x+16
answer: the perpendicular line to y=2/3 x+0 , given the point (8,4) will be:
y=-3/2 x+16
The labor fee is $13.55 and each quart of oil is $2.25
Step-by-step explanation:
Let,
x be the amount of each quart of oil
y be the amount of labor fee
According to given statement;
5x+y=24.80 Eqn 1
7x+y=29.30 Eqn 2
Subtracting Eqn 1 from Eqn 2
![(7x+y)-(5x+y)=29.30-24.80\\7x+y-5x-y=4.50\\2x=4.50](https://tex.z-dn.net/?f=%287x%2By%29-%285x%2By%29%3D29.30-24.80%5C%5C7x%2By-5x-y%3D4.50%5C%5C2x%3D4.50)
Dividing both sides by 2
![\frac{2x}{2}=\frac{4.50}{2}\\x=2.25](https://tex.z-dn.net/?f=%5Cfrac%7B2x%7D%7B2%7D%3D%5Cfrac%7B4.50%7D%7B2%7D%5C%5Cx%3D2.25)
Putting x=2.25 in Eqn 1
![5(2.25)+y=24.80\\11.25+y=24.80\\y=24.80-11.25\\y=13.55](https://tex.z-dn.net/?f=5%282.25%29%2By%3D24.80%5C%5C11.25%2By%3D24.80%5C%5Cy%3D24.80-11.25%5C%5Cy%3D13.55)
The labor fee is $13.55 and each quart of oil is $2.25
Keywords: linear equation, subtraction
Learn more about subtraction at:
#LearnwithBrainly
Refer to the diagram shown below.
The directrix is y = -4 and the focus is (-2, -2).
Therefore the vertex is at (-2, -3).
Consider an arbitrary point (x,y) on the parabola.
The square of distance from the focus to the point is
(x+2)² + (y+2)²
The square of the distance from the point to the directrix is
(y+4)²
Therefore
(y+4)² = (y+2)² + (x+2)²
y² + 8y + 16 = y² + 4y + 4 + (x+2)²
4y = (x+2)² - 12
y = (1/4)(x+2)² - 3
Answer:
Answer:
x =
7
Step-by-step explanation:
= 49
can equal 7 or -7
7 x 7 = 49. -7 x -7 = 49
Answer:
x=103/265 y=18/53
Step-by-step explanation:
5x -9y=1-----------(i)
-7x+2y=-5-----------(ii)
Multiplying eq 1 with 7 gives
35x-63y=7---------eq(iii)
Multiplying eq 2 with 5 gives
-35x+10y=-25--------eq(iv)
adding eq 3 qnd eq 4
35x-63y-35x+10y=7-25
-53y=-18
y=18/53--------eq5
Putting the value of y from eq 5 in eq 1
5x-9(18/53)=-5
5x- 162/53=-5
5x=-5 +162/53
5x= -265+162/53
5x=103/53
x=103/265