We can see that
The given points are on same line.
Further explanation:
There are two methods to find if the given points are on same line
Given points are:
A(1,3) B(4,2) C(-2,4)
We will find the slope of AB, BC, and AC
So,
We can see that
The given points are on same line.
Keywords: Slope, Co linear points
Learn more about slope at:
#LearnwithBrainly
Answer:
(a) x = -0.418 , -3.581
(B) c = 6.855, -1.855
Step-by-step explanation:
(A) We have given equation
On comparing with standard quadratic equation
a = 2, b = 8 and c = 3
So roots of the equation will be
(b)
a = 1, b = -5 and c= -14
So
Answer:
1) (3,5)
2) (4,-7)
3) (6,4)
4) (-4,-3)
Step-by-step explanation:
1)
Subtract y from both sides of the equation.
x = 8 − y
x − y = −2
Replace all occurrences of x in x − y = −2 with 8 − y.
x = 8 − y
(8 − y) − y = −2
Subtract y from −y.
x = 8 − y
8 − 2y = −2
Solve for y in the second equation.
x = 8 − y
y = 5
Replace all occurrences of y in x = 8 − y with 5.
x = 8 −(5)
y = 5
Simplify 8 −(5).
x = 3
y = 5
Slope = (3,5)
2)
Multiply each term by 2 and simplify.
2x+y=12
y+6=−x−4
Move all terms containing variables to the left side of the equation.
2x+y=1x+2
y+6=−4
Move all terms not containing a variable to the right side of the equation.
2x+y=1x+2
y=−10
Multiply each equation by the value that makes the coefficients of x opposite.
2x+y=1(−2)⋅
(x+2y)=(−2)(−10)
Simplify.
2x+y=1−2x−4
y=20
Add the two equations together to eliminate x from the system.
2x+y=1+−2x−4
y=20−3
y=21
Divide each term by −3 and simplify.
y = −7
Substitute the value found for y into one of the original equations, then solve for x.
x = 4
slope (4,-7)
3)
Subtract y from both sides of the equation.
2x−y=8x−y=2
Multiply each equation by the value that makes the coefficients of y opposite
2x−y=8(−1)⋅
(x−y)=(−1)(2)
Simplify. 2x−y=8
−x+y=−2
Add the two equations together to eliminate y from the system.
2x−y=8 + −x+y=−2x=6
Substitute the value found for x into one of the original equations, then solve for y.
y=4
slope (6,4)
4)
Simplify 2(x+1).
y−3=2x+2
y=−3(x+5)
Simplify −3(x+5)
y−3=2x+2
y=−3x−15
Move all terms containing variables to the left side of the equation.
−2x+y−3=2
y=−3x−15
Add 3x to both sides of the equation.
−2x+y−3=2
y+3x=−15
Move all terms not containing a variable to the right side of the equation.
−2x+y=5
y+3x=−15
Reorder the polynomial.
−2x+y=5
3x + y=−15
Multiply each equation by the value that makes the coefficients of y opposite.
−2x+y=5(−1)⋅
(3x+y)=(−1)(−15)
Simplify.
−2x+y=5
−3x−y=15
Add the two equations together to eliminate y from the system.
−2x+y=5 + −3x−y=15−5x=20
Divide each term by −5 and simplify.
x=−4
Substitute the value found for x into one of the original equations, then solve for y.
y=−3
slope (-4,-3)
