Question

What is the intersection of y = 3x +4 and y = -2x +1

Answer 1

Both linear functions will intersect at the same point, meaning, the x y coordinates are the same. So you have to equate both equations and clear the value of x:

`\begin{gathered} 3x+4=-2x+1 \\ 3x+2x=1-4 \\ 5x=-3 \\ x=(-3)/(5) \end{gathered}`

Now using either function you have to calculate the value of the corresponding y-coordinate, for explanation purposes I'll do it with both:

`\begin{gathered} y=3x+4 \\ y=3\cdot((-3)/(5))+4=(11)/(5) \end{gathered}`

`\begin{gathered} y=-2x+1 \\ y=-2((-3)/(5))+1=(11)/(5) \end{gathered}`

As you see, using either function to calculate the y-coordinate is the same.

The functions intersect in point (-3/5, 11/5)