Explanation:
You want to show that the line through (a, 0) and (0, b) has equation ...
x/a +y/b = 1
Slope
The slope of the line through the given points is found using the slope formula:
m = (y1 -y1)/(x2 -x1) = (b -0)/(0 -a) = -b/a
Slope-intercept equation
The y-intercept is given as 'b', so the slope-intercept equation is ...
y = -b/ax +b
Dividing by b, we get ...
y/b = -x/a +1
and adding x/a gives the desired form:
x/a +y/b = 1
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Additional comment
This equation is the "intercept form" equation of a line. It lets you write the equation of the line if you know the intercepts. Like other specialized forms of the equation for a line, it can be useful on occasion.
