Perpendicular lines refers to a pair of straight lines that intercept each other. The slopes of this lines are opposite reciprocal, meaning that it's multiplication is -1.
On this case they give you the equation of a line and a point, and is asked to find the equation of a line that is perpendicular to the given one, and that passes through this point.
-2x+3y=-6 Add 2x in both sides
3y=2x-6 Divide by 3 in both sides to isolate y
y=2/3x-6/3
The slope of the given line is 2/3, which means that the slope of a line perpendicular to this one, needs to be -3/2. Now you need to find the value of b or the y-intercept by substituting the given point into the formula y=mx+b, where letter m represents the slope.
y=mx+b Substitute the given point and the previous slope found
-2=(-3/2)(6)+b Combine like terms
-2=-9+b Add 9 in both sides to isolate b
7=b
The equation that represents the line perpendicular to -2x+3y=-6 and that passes through the point (6,-2), is y=-3/2x+7.
Answer:
3 hours walking dogs and 5 hours landscaping
Step-by-step explanation:
Answer: 239
Step-by-step explanation:
![g(7)=2(7)-5=9\\\\f[g(7)]=f(9)=3(9)^2 - 4=239](https://tex.z-dn.net/?f=g%287%29%3D2%287%29-5%3D9%5C%5C%5C%5Cf%5Bg%287%29%5D%3Df%289%29%3D3%289%29%5E2%20-%204%3D239)
The factors of 20 are 1,2,3,5,6,10,15, and 30
6+3=9.
