- Slope-Intercept Form: y = mx+b, with m = slope and b = y-intercept
So perpendicular lines have <u>slopes that are negative reciprocals</u> to each other, but firstly we need to find the slope of the original equation. The easiest method to find it is to convert this standard form into slope-intercept.
Firstly, subtract 3x on both sides of the equation: ![-4y=-3x+9](https://tex.z-dn.net/?f=%20-4y%3D-3x%2B9%20)
Next, divide both sides by -4 and your slope-intercept form of the original equation is ![y=\frac{3}{4}x-\frac{9}{4}](https://tex.z-dn.net/?f=%20y%3D%5Cfrac%7B3%7D%7B4%7Dx-%5Cfrac%7B9%7D%7B4%7D%20)
Now looking at this equation, we see that the slope is 3/4. Now since our new line is perpendicular, this means that <em>its slope is -4/3.</em>
Now that we have the slope, plug that into the m variable and plug in (-4,-5) into the x and y coordinates to solve for the b variable as such:
![-5=-\frac{4}{3}*-4+b\\\\-5=5\frac{1}{3}+b\\\\-10\frac{1}{3}=b](https://tex.z-dn.net/?f=%20-5%3D-%5Cfrac%7B4%7D%7B3%7D%2A-4%2Bb%5C%5C%5C%5C-5%3D5%5Cfrac%7B1%7D%7B3%7D%2Bb%5C%5C%5C%5C-10%5Cfrac%7B1%7D%7B3%7D%3Db%20)
<u>In short, your new equation is y = -4/3x - 10 1/3.</u>
Answer:
x=4.5
Step-by-step explanation:
Given the equation
, we simplify as:
![\frac{3}{5}(30x-15)=72\\\\18x-9=72](https://tex.z-dn.net/?f=%5Cfrac%7B3%7D%7B5%7D%2830x-15%29%3D72%5C%5C%5C%5C18x-9%3D72)
#We further simplify as multiples of 9(divide by 9 to solve for x):
![18x-9=72\\\\2x-1=8\\\\2x=9\\\\x=4.5](https://tex.z-dn.net/?f=18x-9%3D72%5C%5C%5C%5C2x-1%3D8%5C%5C%5C%5C2x%3D9%5C%5C%5C%5Cx%3D4.5)
Hence, from our simplification the equation has the same value as x=4.5
Well if she earned the same amount per hour the hours can be added. 2.25 + 3.25 = 5.5 hours. To get the rate of earning per hour you would then divide the total made by the total time worked. 42/5.5 = $7.64 approximately.
Answer:
He would pay a total of $21.50
Step-by-step explanation:
A trick that I learned is to take the zeros and decimals off. Then multiply. Ex) 75 × 2 =150. Take away the zero (15) and ad the decimal (1.5)
I'm not the best at explaining but I hope this helps
Answer:
Option 1
Step-by-step explanation:
5(3x+2) + 2(x-7)
15x + 10 + 2x -14
15x + 2x + 10 - 14
17x - 4