Question

Write an equation in standard form for the line that passes through the given points.

(2, 7) and (-5, 2)

Answer 1

So, pretend this is your x-axis and y-axis:

I

I

(-2,7) • I

I

I • (2, 5)

I

I

I

I

_________________I____________________

I

I

I

TO GET FROM POINT (-2, 7) TO POINT (2, 5), WE MOVE DOWN 2 AND OVER 4, SO THE SLOPE IS -1/2. IF WE FOLLOW THAT SLOPE AND MOVE DOWN 1 AND OVER 2 FROM THE FIRST POINT OF (-2, 7), WE WILL LAND ON A POINT LOCATED AT (0, 6), WHICH WOULD BE THE "Y-INTERCEPT". WE WERE JUST ABLE TO CALCULATE THE SLOPE OF THE LINE AND THEN USE THE SLOPE TO FIND THE INTERCEPT. SO, THE "SLOPE-INTERCEPT" FORM OF THE EQUATION FOR THIS LINE IS:

y = -1/2x + 6

TO RE-WRITE THIS IN STANDARD FORM, WE JUST WANT TO MOVE THE X VARIABLE OVER TO THE LEFT WITH THE Y VARIABLE, SO:

y = -1/2x + 6

+1/2x + 1/2x

1/2x + y = 6 .... and that is your answer!