Mathematics Slope Mh
1 answer:
Answer:
y = - 2x - 6
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 )
Calculate m using the slope formula
m = (y₂ - y₁ ) / (x₂ - x₁ )
with (x₁, y₁ ) = (- 2, - 2) and (x₂, y₂ ) = (1, - 8)
m = =
= - 2, thus
y = - 2x + c ← is the partial equation
To find c substitute either of the 2 points into the partial equation
Using (- 2, - 2), then
- 2 = 4 + c ⇒ c = - 2 - 4 = - 6
y = - 2x - 6 ← equation of line
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ANSWER
72 square feet
EXPLANATION
The perimeter of a rectangle is given by:
P= 2l+2w
It was given that, the perimeter of the rectangular mat, is 36 feet.
36= 2l+2w
Divide through by 2.
It was given also that, the length of the mat is twice its width.
This implies that,
Put equation (2) into equation (1) to get,
This means that the length is 12 ft.
The area of the rectangular mat is
72 square feet
EXPLANATION
The perimeter of a rectangle is given by:
P= 2l+2w
It was given that, the perimeter of the rectangular mat, is 36 feet.
36= 2l+2w
Divide through by 2.
It was given also that, the length of the mat is twice its width.
This implies that,
Put equation (2) into equation (1) to get,
This means that the length is 12 ft.
The area of the rectangular mat is
Answer:
a: no solutions
b: (2, 3)
Step-by-step explanation:
a:
In both equations, the slope of x is the same, but the y-intercept is not, which means they are parallel. Therefore, this system of equations has no solutions.
b:
Since both of the equations are equal to y, we can set them equal to each other:
We can solve by factoring (by finding a number that multiplies to 4 and adds up to -4):
(x-2)^2 = 0
x = 2
Now, to find y, plug-in x to any of the equations:
y = 2*2-1 = 3
Therefore, the solution to this system of equation is (2, 3)
I hope this helped.