Question

What is the equation of the line that passes through points (0,1) and (3, 0)?

Answer 1

See the answer below...

Explanation:

To discuss this question, let a arbitrary point `"P"(x,y)` with whose respect we will determine the equation of the straight line.

• The slope of a straight line is determined by the following step:-

  If there is two point `"M"(x_1,y_1)` and `"N"(x_2,y_2)` passes through a straight line,the `color(red)("slope of the line"` will be `ul(bar(|color(red)(m=(y_2-y_1)/(x_2-x_1))|`

• So, we can easily determine the slope of the line by using the above formula. We have variables also to determine slope.

  1) The slope of the line in one hand is
  `color(green)(m=(0-1)/(3-0)=-1/3` where `x_1=0;x_2=3;y_1=1;y_2=0`
  2)The slope of the straight line again is `color(violet)(m=(y-1)/(x-0)=(y-1)/x` where `x_1=0;x_2=x;y_1=1;y_2=y`

Now, we can equalize the slope i.e,

`(y-1)/x=-1/3`
`=>3-3y=x`
`=>color(red)(ul(bar(|color(black)(x+3y=3)|`

Hope the answer helps...
Thank you...

which process I did it, I did not tell you.

It is Two point form.