SOLUTION: please help me solve this problem: "write the equation of a line that passes through (21,-40) and has a slope of 4/5" i need to find the equation of the line

Algebra ->  Equations -> SOLUTION: please help me solve this problem: "write the equation of a line that passes through (21,-40) and has a slope of 4/5" i need to find the equation of the line       Log On


   



Question 701518: please help me solve this problem: "write the equation of a line that passes through (21,-40) and has a slope of 4/5" i need to find the equation of the line
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
If you know the highlight%28slope%29, m, and the coordinates of a highlight%28point%29, (a,b),
the equation of the line can be written as
y-b=m%28x-a%29
That is called the highlight%28point%29-highlight%28slope%29 form of the equation of the line.
It is derived from the definition of highlight%28slope%29
as the difference in y-coordinates divided by
difference in x-coordinates for any pair of points on the line.
For any unknown point (x,y) and a known point (a,b),
their coordinates and the slope, m, are related by
%28y-b%29%2F%28x-a%29=m --> y-b=m%28x-a%29

For your problem,
y-%28-40%29=%284%2F5%29%28x-21%29 --> highlight%28y%2B40=%284%2F5%29%28x-21%29%29
That is one of the infinite number of equivalent equations for the line.
It can be transformed into the unique slope-intercept form of the equation for the line.
y%2B40=%284%2F5%29%28x-21%29 --> y%2B40=%284%2F5%29x-21%284%2F5%29 --> y%2B40=%284%2F5%29x-84%2F5 --> y=%284%2F5%29x-84%2F5-40 --> y=%284%2F5%29x-84%2F5-200%2F5 --> highlight%28y=%284%2F5%29x-284%2F5%29 (in slope-intercept form)