the equation 6x -18y = 18 is an equation of a straight line
the x intercept is the point on the X axis when y = 0
The y intercept is the point on the Y axis when x = 0
Therfore first setting y = 0 the equation becomes 6x = 18; divide both sides by 6 and you get x =3;
the point ( x,y) or ( 3,0) lies on the X axis and it called the x intercept
to find the y intercept, set x = 0 in the equation and you get, -18y=18; divide both sides by -18 then
y= -1; the point (x,y) or (0, -1) lies on the Y axis and it is called the y intercept
for the two points ( 3,0) and (0,-1) plotted on a cartesian system of coordinates you get a line passing through point (3,0) on the X axis and the point (0,-1) on the Y axis
To find the slope of that line divide the difference between the Y coordinates by the difference between the x coordinates. that is
Slope = (y2-y1)/(x2-x1) = ( -1-0)/(0-3) = -1/-3 = 1/3
the equation of the line would be a function of the slope and anypoint that passes through the line
Lets try first the slope and the x intercept (3,0)
The equation of the line would be, Slope = (y-0)/(x-3) = 1/3
Solving 1/3(x-3)=y, and y=(1/3)x-3(1/3), then y=(1/3)x-1
Lets try now the slope and te y intercept (0,-1)
The equation of the line would be, Slope = (y-(-1))/(x-0) = y+1/x = 1/3
Solving y+1 = (1/3) x , and y = (1/3)x -1
and either point and slope lead to the same equation of a straigth line of the form y=mx+b
Where m = 1/3 is the slope. and b = -1 is the y intercept of that line.
