please solve all genius do it
Answers
Answer:
The line y=mx passes through the origin.....(given)
i.e it passes through (0,0).
Putting (x,y)=(0,0) in the given equation therefore
0=m×0
⟹0=0. ....
So the given assertion is true....
now there should be one more question in your mind that.....
Why does a line not pass through the origin in a graph?
so ans- as uk that lines on graphs are produced by three kinds of equations. The first type is x = a, where a is a real number. For an equation of this type to produce a line that goes through the origin, it would have to be x = 0. The second type is y=a. For an equation of this type to produce a line, it would have to be y = 0.
The third type is y = mx + b. In this type, b dictates where the graph crosses the y axis. So for the line graph for this type to include the origin, b must = 0. If b is any other number, the line graph will not pass through the origin....
Okay, let’s look at it in this another way: when does a line pass through the origin? The line represents possible values of x and y that satisfy the equation.
So, when a line passes through the origin, it passes through the coordinates (0,0). x = 0, y = 0. So, let’s model this with the equation ax + by + c = 0. Sub in x = 0 and y = 0 to the equation and we find that 0 + 0 + c = 0. Clearly, c = 0.
So, with this simple explanation, I hope you understand when a line does pass through the origin.
Now, let’s look at when a line doesn’t pass through the origin. This is when c is not equal to 0. Hence, when x = 0, y cannot equal 0; c + by = 0, and we know that c is not 0. If y is 0, then we get c = 0… where c is not 0. Ehh. Thus, you can see that a line does not pass through the origin when c is not equal to 0 by ehat is hope is a simple explanation. You don’t need to know how to prove it, I presume, but that’s not too hard either.
Oops, I realised that I just assumed you were talking about linear graphs. For quadratic graphs, the reasoning is similar. For graphs of the form y = ax^2, the minimum/maximum point of the graph will be the origin. For graphs of the form y = ax^2 + bx, it will pass through the origin but the line of symmetry will be different. For graphs of the form y = ax^2 + bx + c (you know, where c is not zero) , the graph will not pass through the origin because the maximum/ minimum point is actually raised or lowered by c units.....