<h3>
7.</h3><h3>
The required equation of the line is y= 2x-5</h3><h3>
8.</h3><h3>
y=30</h3>
Step-by-step explanation:
Given , a line passes through the points (1,-3) and (3,1)
The equation of line which passes through the points
and
is
![y - y_1=\frac{y_2-y_1}{x_2-x_1} (x-x_1)](https://tex.z-dn.net/?f=y%20-%20y_1%3D%5Cfrac%7By_2-y_1%7D%7Bx_2-x_1%7D%20%28x-x_1%29)
Here
and ![x_2 = 3 , y_2= 1](https://tex.z-dn.net/?f=x_2%20%3D%203%20%2C%20y_2%3D%201)
The required equation of the line is
![y+3=\frac{1+3}{3-1} (x-1)](https://tex.z-dn.net/?f=y%2B3%3D%5Cfrac%7B1%2B3%7D%7B3-1%7D%20%28x-1%29)
![\Leftrightarrow y +3 =2(x-1)](https://tex.z-dn.net/?f=%5CLeftrightarrow%20y%20%2B3%20%3D2%28x-1%29)
![\Leftrightarrow y =2x-2-3](https://tex.z-dn.net/?f=%5CLeftrightarrow%20y%20%3D2x-2-3)
![\Leftrightarrow y =2x-5](https://tex.z-dn.net/?f=%5CLeftrightarrow%20y%20%3D2x-5)
8.
Given, y varies directly with x and y=24 when x=8
Therefore,
![y\propto x](https://tex.z-dn.net/?f=y%5Cpropto%20x)
.........(1)
y = 24 when x=8
![\therefore 24 = 8k](https://tex.z-dn.net/?f=%5Ctherefore%2024%20%3D%208k)
![\Rightarrow k =3](https://tex.z-dn.net/?f=%5CRightarrow%20k%20%3D3)
Equation (1) becomes
y= 3x
So, when x=10
y=3×10
⇒y=30
Answer:
y = 2
Step-by-step explanation:
When line is horizontal, all points on this line have the same value of y.
In this case , all points have to have y = 2.
y = 2, is an equation of horizontal line.
Answer:area=l×b
10×8=80cm* 2
perimeter =(l+b)2
10+8)*2
18×2
=36cm
Step-by-step explanation:
X+y=28
xy=7
xy=7
divide both sides by x
y=7/x
sub 7/x for y in first equation
7/x+x=28
times both sides by x
7+x^2=28x
minus 28x from both sides
x^2-28x+7=0
use quadratic formula
if
ax^2+bx+c=0
x=
![\frac{-b+/- \sqrt{b^2-4ac} }{2a}](https://tex.z-dn.net/?f=%20%5Cfrac%7B-b%2B%2F-%20%5Csqrt%7Bb%5E2-4ac%7D%20%7D%7B2a%7D%20)
x=
![\frac{-(-28)+/- \sqrt{(-28)^2-4(1)(7)} }{2(1)}](https://tex.z-dn.net/?f=%20%5Cfrac%7B-%28-28%29%2B%2F-%20%5Csqrt%7B%28-28%29%5E2-4%281%29%287%29%7D%20%7D%7B2%281%29%7D%20)
x=
![14+/- 3\sqrt{21}](https://tex.z-dn.net/?f=%2014%2B%2F-%203%5Csqrt%7B21%7D%20)
sub for y
y=7/x
y=
![\frac{7}{14+/-3 \sqrt{21} }](https://tex.z-dn.net/?f=%20%5Cfrac%7B7%7D%7B14%2B%2F-3%20%5Csqrt%7B21%7D%20%7D%20)
the reciprocals are
![\frac{14+/-3 \sqrt{21} }{7}](https://tex.z-dn.net/?f=%20%5Cfrac%7B14%2B%2F-3%20%5Csqrt%7B21%7D%20%7D%7B7%7D%20)
and
![\frac{1}{14+/-3 \sqrt{21} }](https://tex.z-dn.net/?f=%20%5Cfrac%7B1%7D%7B14%2B%2F-3%20%5Csqrt%7B21%7D%20%7D%20)
times first one by
![\frac{14+/-3 \sqrt{21} }{14+/-3 \sqrt{21} }](https://tex.z-dn.net/?f=%20%5Cfrac%7B14%2B%2F-3%20%5Csqrt%7B21%7D%20%7D%7B14%2B%2F-3%20%5Csqrt%7B21%7D%20%7D%20)
and second by 7/7
![\frac{(14+/-3 \sqrt{21} )(14+/-3 \sqrt{21} )+7}{(7)(14+/-3 \sqrt{21} )}](https://tex.z-dn.net/?f=%20%5Cfrac%7B%2814%2B%2F-3%20%5Csqrt%7B21%7D%20%29%2814%2B%2F-3%20%5Csqrt%7B21%7D%20%29%2B7%7D%7B%287%29%2814%2B%2F-3%20%5Csqrt%7B21%7D%20%29%7D%20)
evaluate the plus and minus yourself please, my head hurts
Ok so you can take this as a substitution problem.
x=-2y-13
then substitute
12(-2y-13)+5y=-4
--24y-13×12+5y=-4
sorry i gotta go