Use algebra to find the point at which the line k(x)=-9/5x-41/10 intersects the line g(x)=4/3x+103/15

Answer 1

We have two functions: k(x)=(-9/5)x-(41/10) and g(x)=(4/3)x+(103/15). We want to use algebra to find the point of intersection. That is where the two lines cross each other. At that point, the same input, or x-value, gets out the same y-value for both both functions. So what we want to do is set the two functions equal to each other and solve for x. Once we have an x-value, we can plug that number into either function to get the y-value. So we have:

(-9/5)x-(41/10) = (4/3)x+(103/15) add (41/10) to both sides to get

(-9/5)x = (4/3)x+(329/30) subtract (4/3)x from both sides to get

(-47/15)x = 329/30 now multiply both sides by (-15/47) to isolate x and get

x = -3.5

To find the y-value, just plug x=-3.5 into either function to get 2.2.

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