Answer:
x + 10 = 4x
Step-by-step explanation:
Let x = her age 10 years ago.
Her age now is x + 10.
x + 10 = 4x
Answer:
Step-by-step explanation:
y = -2x+5
slope of line is -2.
slope of parallel to line is also -2
point-slope equation for line of slope -2 that passes through (-5,3):
y-3 = -2(x+5)
The equation of line perpendicular to given line through (-6,7) is:
![y=\frac{1}{6}x+8](https://tex.z-dn.net/?f=y%3D%5Cfrac%7B1%7D%7B6%7Dx%2B8)
Further explanation:
Given equation of line is:
![6x+y=3\\y= -6x+3](https://tex.z-dn.net/?f=6x%2By%3D3%5C%5Cy%3D%20-6x%2B3)
The co-efficient of x is the slope of given line.
Let m1 be the slope of given line
and
m2 be the slope of line perpendicular to given line
Then
![m_1=-6](https://tex.z-dn.net/?f=m_1%3D-6)
Product of slopes of perpendicular lines is -1
![m_1*m_2 = -1\\-6*m_2=-1\\m_2=\frac{-1}{-6}\\m_2=\frac{1}6}](https://tex.z-dn.net/?f=m_1%2Am_2%20%3D%20-1%5C%5C-6%2Am_2%3D-1%5C%5Cm_2%3D%5Cfrac%7B-1%7D%7B-6%7D%5C%5Cm_2%3D%5Cfrac%7B1%7D6%7D)
The equation of new line can be written as:
![y=m_2x+b\\](https://tex.z-dn.net/?f=y%3Dm_2x%2Bb%5C%5C)
Putting m2
![y=\frac{1}{6}x+b](https://tex.z-dn.net/?f=y%3D%5Cfrac%7B1%7D%7B6%7Dx%2Bb)
To find the value of b, we will put (-6,7) in equation
![7=\frac{1}{6}(-6)+b\\7=-1+b\\b=7+1\\b=8](https://tex.z-dn.net/?f=7%3D%5Cfrac%7B1%7D%7B6%7D%28-6%29%2Bb%5C%5C7%3D-1%2Bb%5C%5Cb%3D7%2B1%5C%5Cb%3D8)
Putting the values of b and m in general equation
![y=\frac{1}{6}x+8](https://tex.z-dn.net/?f=y%3D%5Cfrac%7B1%7D%7B6%7Dx%2B8)
Keywords: Slope, Point-slope form, perpendicular lines
Learn more about perpendicular lines at:
#LearnwithBrainly
In order to invert a function, switch y and x in the definition, and solve for y again:
![y=2x+1 \mapsto x=2y+1](https://tex.z-dn.net/?f=y%3D2x%2B1%20%5Cmapsto%20x%3D2y%2B1)
Solving for y, we have
![x=2y+1\iff x-1=2y \iff y=\dfrac{x-1}{2}](https://tex.z-dn.net/?f=x%3D2y%2B1%5Ciff%20x-1%3D2y%20%5Ciff%20y%3D%5Cdfrac%7Bx-1%7D%7B2%7D)