What is the slope of the line that has an x-intercept 8 and a y-intercept 15?

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justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

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

giorgiana1976's profile pic

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

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.

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