Linear Equations and Matrix Operations

[zaq102101]

Taken from a recent assigment:

"Consider the equation of a line in Slope-Intercept form, y=ax+b, where "a" is the slope of the line, and "b" is the y-intercept. Consider writing it in the form xa+b=y where each x and y will be given as a point on the line, and given two points a system of two equations may be solved for "a" and "b". Given the points (x1,y1) and (x2,y2), write a system of linear equations in standard form to be solved for "a" and 'b". Write the augmented matrix to be row reduced by Gaussian Elimination to solve for "a" and "b". Now perform the row reduction by hand to get formulas for "a" and "b". Compare the formula you got for "a" with the one you already know for the slope of a line."

I'm stuck at making the system of equations. I can move some of the variables around but I don't feel like it's going anywhere. I know gaussian elimination and the formula it refers to in the last sentence but I can't get to that anyway. Anyone have any idea what I'm supposed to do here?

 

[Deleted member 4993]

Re: Completely Lost, Linear Equations and Matrix Operations

Taken from a recent assigment:

"Consider the equation of a line in Slope-Intercept form,
y=ax+b,
where "a" is the slope of the line, and "b" is the y-intercept. Consider writing it in the form
xa+b=y
where each x and y will be given as a point on the line, and given two points a system of two equations may be solved for "a" and "b". Given the points (x1,y1) and (x2,y2), write a system of linear equations in standard form to be solved for "a" and 'b". Write the augmented matrix to be row reduced by Gaussian Elimination to solve for "a" and "b". Now perform the row reduction by hand to get formulas for "a" and "b". Compare the formula you got for "a" with the one you already know for the slope of a line."

I'm stuck at making the system of equations. I can move some of the variables around but I don't feel like it's going anywhere. I know gaussian elimination and the formula it refers to in the last sentence but I can't get to that anyway. Anyone have any idea what I'm supposed to do here?

This is a fairly standard problem - you do not need Gaussian elimination (per se) - but you can do it.

For ease of writing let us call

p = x[sub:2y04jkji]1[/sub:2y04jkji] and q = y[sub:2y04jkji]1[/sub:2y04jkji]

and

u = x[sub:2y04jkji]2[/sub:2y04jkji] and v = y[sub:2y04jkji]2[/sub:2y04jkji]

Then

ap+ b = q

au + b = v

Augmented matrix

p   1   q
u   1   v

Now continue....

Please show us your work, indicating exactly where you are stuck - so that we know where to begin to help you.