What is the slope of the line that has an x-intercept 8 and a y-intercept 15?
The given line has its x-intercept at 8 and the y-intercept at 15. There are many ways to solve for the slope. Here is a relatively simple way. Use the intercept - intercept form of the line which is x/a + y/b = 1, where a and b are the x and y intercepts.
x/8 + y/15 = 1
=> 15x + 8y = 120
Now convert this to slope intercept form y = m*x + c
15x + 8y = 120
=> 8y = -15x + 120
=> y = (-15/8)*x + 120/8
The slope is -15/8
The slope of the given line is -15/8
We know that a line is intercepting x axis in the point (x,0) and it is intercepting y axis in the point (0,y).
We'll write the general form of a line:
y = ax + b
We know that the line is intersecting x axis in x = 8.
0 = 8a + b
8a = -b
a = -b/8
We also know that the line is intecrepting y axis in y = 15.
15 = b
a = -15/8
We also know that the slope of the line is given by the coefficient of x (when the equation of the line is written in the slope point form: y=mx + n)
Comparing, we'll get a = m = -15/8
The slope of the line whos x intercept is 8 and y intercept is 15, is m = -15/8.