Answer:
y = 1.6x + 3.4
Step-by-step explanation:
We have to use the equation y = m x + c to find the equation of the line.
Here,
m ⇒ slope
c ⇒ y-intercept
<u>First, let us find the slope.</u>
For that, we can use the given two coordinates.
( -1 , 5 ) ⇒ ( x₁ , y₁ )
( 4 , -3 ) ⇒ ( x₂ , y₂ )
The <u>formula to find the slope</u> of a line is :
m = ( y₁ - y₂ ) ÷ ( x₁ - x₂ )
<u>Let us solve now.</u>
m = ( y₁ - y₂ ) ÷ ( x₁ - x₂ )
m = ( 5 - ( -3 ) ) ÷ ( -1 - 4 )
m = ( 5 + 3 ) ÷ -5
m = 8 ÷ -5
<u>m = -1.6</u>
Now let us<u> find the y-intercept (c )</u> of the line.
For that, let us get one of the coordinates which are given in the question.
I'll get ( -1 , 5 ) from that.
( -1 , 5 ) ⇒ ( x , y )
<u>Let us solve now.</u>
y = mx + c
5 = -1.6 × -1 + c
5 = 1.6 + c
5 - 1.6 = c
<u>3.4 = c</u>
Therefore,
m ⇒ -1.6
c ⇒ 3.4
So, the equation of the line is :
y = mx + c
<u>y = 1.6x + 3.4</u>
Answer: 18
Step-by-step explanation: You would substitute x for 3 in the expression. This would equal 21-3, or 18 when simplified
Just like at any other time, to add/subtract fractions you need a common denominator.
14)
1/(x^2+2x)+(x-1)/x=1 so we need a common denominator of x(x^2+2x)
[1(x)]/(x(x^2+2x))+[(x-1)(x^2+2x)]/(x(x^2+2x))=[1(x(x^2+2x))]/(x(x^2+2x))
now if you multiply both sides of the equation by x(x^2+2x) you are left with:
x+(x-1)(x^2+2x)=x(x^2+2x)
x+x^3+2x^2-x^2-2x=x^3+2x^2
x^3+x^2-x=x^3-2x^2
x^2-x=-2x^2
3x^2-x=0
x(3x-1)=0, x=0 is an extraneous solution as division by zero is undefined. So the only real solution is:
x=1/3
...
16)
(r+5)/(r^2-2r)-1=1/(r^2-2r) the common denominator we need r^2-2r so
[r+5-1(r^2-2r)]/(r^2-2r)=1/(r^2-2r), multiplying both sides by r^2-2r yields:
r+5-r^2+2r=1
-r^2+3r+5=1
-r^2+3r+4=0
r^2-3r-4=0
(r-4)(r+1)=0, r^2-2r cannot equal zero, r(r-2)=0, r cannot equal 0 or 2...
r=-1 or 4
Answer:
Infinite solutions
Step-by-step explanation:
Any value of x makes the equation true
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∞
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∞
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