In this post, we will find the graph of y=4/x. When a equals 4, the equation simplifies to y=1. Plotting the point (0, 1) and graphing it on a coordinate plane produces an interesting result:

## The line is vertical!

To find the intersection point where x=0 and y=-a, solve for x: 0 = -a a. Recall that dividing by negative numbers reverses the sign of both variables. So a is positive when x=0 and so (x,-a) is the solution to our equation.

Plotting this vertical line on a coordinate plane produces an interesting result: The line is vertical! Notice how it does not intersect with any other lines or points. In fact, this graph only contains one point at all–the origin! What happens if we change the value of a? For example, what would happen if we plugged in another number such as 12 into our original equation? We will explore more questions about this in Part II.

To find the intersection point where x=0 and y=-a, solve for x: 0 = -12 __ 12. Recall that dividing by negative numbers reverses the sign of both variables. So a is positive when x=0 and so (x,-a) is not even our solution! We now have to solve for (-12), which means we need to flip it upside down on our coordinate plane–or in other words turn it into two multiplied by itself or rearrange as “a times (-12)–which yields zero! In short, there are no intersections between this line with any other lines or points on the graph because its vertical nature dictates that all points will be off of the graph entirely regardless of their coordinates!

To find the intersection point where x=-a and y=0, solve for (-12): 12 = -36 __ 36. Recall that dividing by negative numbers reverses the sign of both variables so a is positive when x=-a and so (x,-a) is our solution! In short, there are two intersections between this line with any other lines or points on the graph because its vertical nature dictates that all points will be off of the graph entirely regardless of their coordinates.

### In summary: y values get bigger as you move up towards 0

We have two solutions in general case when we only know one variable-(x,y)–and want to determine whether it intersects with another function in cases where the other function is a linear equation. *If we increase our constants by one, then every point on this line and all lines parallel to it will be reversed in relation with each other–for example if a=y for some unknown x, b=-x–then (-a,-b) would have been considered a solution to the first case but becomes an “intersection” point in this general case

The graph of y=ax+by does not change much when you change either variable since both variables multiply together as usual. This makes sense because that’s what happens with these two equations: ax+by = (ax)(-b)+(-ay)(-b)=0

Graph entirely regardless of their coordinates! Each point on the line will have the same slope as described by its equation.

Graph entirely regardless of their coordinates! Each point on the line will have the same slope as described by its equation. Consider all points, including those outside this domain. In order to plot a linear function in any system, one needs only give it an appropriate x and accordingly for every other coordinate axis besides y–x is always assumed constant so there are no issues plotting them on the same graph.

### Consider all points, including those outside this domain.

In order to plot a linear function in any system, one needs only give it an appropriate x and accordingly for every other coordinate axis besides y–x is always assumed constant so there are no issues plotting them on the same graph. What about when encountering cases where both variables have different slopes? Consider the case of ax+by=c:

ax*(-b)+(-ay)(-b)=0 but also c*a=-y which means that (-ay)/-(-b)=-c/a = -e cancel out giving us (cb)/(-ab)=(ca)/(-ba). The rate equation has now changed into how fast these two equations will converge to the solution.

Consider when a=b: if they are equal, then this is actually just one line on the graph that has an infinite slope and convergence at one point (the origin). If it does not cross any other lines of y=mx+c or x=-y-a and therefore intersects both these curves only once, which means their slopes should be identical. When zoomed into the plot, there will be two points where the x–axis intercepts with the curve. One is at its start point and another as it approaches infinity from below; for every vertical distance up between them represents how many units they have diverged in terms of rate

(cb)/(-ab)=(ca)/(-ab)

### If these two equations have a common denominator, they will converge to the same solution.

In other words, if you graph them on the same coordinates and zoom in enough so that it becomes clear which is ‘ahead’ or has been moving faster than the other one for any length of time (as x–>infinity), then you’ll find that eventually both are coming together at a single point. And when this happens, their slopes should also be identical because there’s only one line at infinity where all points are equidistant from each other; i.e., y=mx+c can’t diverge as x goes to infinity just like how

-x/y=-a/(bx)+=(-a)/(bx)+

i.e., y=mx+c can’t converge as x goes to infinity just like how

-x/y=-a/(bx)=>(-ax + b)/ (by)=0, so the lines will always be perpendicular and their slopes are identical. This is true even if you have a line that’s not identified with equation form such as in the example of m=(g)(h). The slope would still become zero at some point because each variable has an inverse function that produces the same result when multiplied by one another; for g=m^-n*k, h=m^n*l, then gh = ml == 0->infinity or vice versa.

-x/y=-a/(bx)=0, so the lines will always be perpendicular and their slopes are identical. This is true even if you have a line that’s not identified with equation form such as in the example of m=(g)(h). The slope would still become zero at some point because each variable has an inverse function that produces the same result when multiplied by one another; for g=m^-n*k, h=m^n*l, then gh = ml == 0->infinity or vice versa.

### The graph y=mx+c can’t diverge just like how -x/y=-a/( b x)=>(-ax + b)/ (by)=0, so the lines will always be perpendicular.

x/y=-a/(bx)=0, so the lines will always be perpendicular and their slopes are identical. This is true even if you have a line that’s not identified with equation form such as in the example of m=(g)(h). The slope would still become zero at some point because each variable has an inverse function that produces the same result when multiplied by one another; for g=m^-n*k, h=m^n*l, then gh = ml == 0->infinity or vice versa.-x/y=-a/( b x)=>(-ax + b)/ (by)=0, so the lines will always be perpendicular. -x/y=-a/(bx)=0, so the lines will always be perpendicular and their slopes are identical. This is true even if you have a line that’s not identified with equation form such as in the example of m=(g)(h). The slope would still become zero at some point because each variable has an inverse function that produces the same result when multiplied by one another; for g=m^-n*k, h=m^n*l, then gh = ml == 0->infinity or vice versa.-x/y=-a/( b x)=>(-ax + b)/ (by)=0, so the lines will always be perpendicular. This means all derivatives can’t diver