What is the x and y intercepts of 3x - 8y - 45 = 0
The x and y intercepts of the line given by the equation 3x - 8y - 45 = 0 have to be determined.
Rewrite the equation of the line in the form `x/a + y/b = 1` where a and b are the x and y intercepts respectively.
3x - 8y - 45 = 0
=> 3x - 8y = 45
=> `(3x)/45 - (8y)/45 = 1`
=> `x/(45/3) - y/(45/8) = 1`
=> `x/15 - y/5.625 = 1`
The x-intercept of the line is 15 and the y-intercept is 5.625
The x- and y-intercepts can be found simply by plugging in "0" for the x and y values:
So, since the "y" value of the x-int. will be 0 (x,0), you can plug in 0 for y:
3x-8(0)-45=0, so now just solve for x which gives you 15 for the x-intercept or (15,0)
Now, for the y-intercept, you can do the opposite and plug in 0 for the "x":
And solving for y will give you -5.625 or -8/45 which is also (0,-5.625) for the y-int.
Therefore, the x-int is (15,0) and the y-int is (0,5.625) as shown in the graph: