What is the equation of a line that has an x-intercept 8 and a y-intercept 7.

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justaguide | College Teacher | (Level 2) Distinguished Educator

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The equation of a line that has an x-intercept a and a y-intercept b is given by `x/a + y/b = 1` .

As a confirmation, if the x-intercept is a, the line passes through (a, 0) and if the y-intercept is b, the line passes through (0, b). An angle passing through (a, 0) and (0, b) has an equation (y - 0)/(x - a) = (0 - a)/b

=> y/(x - a) = b/-a

=> y/b = (x - a)/-a

=> y/b = -x/a + 1

=> x/a + y/b = 1

Here, the x-intercept is 8 and the y-intercept is 7.

The equation of the line is x/8 + y/7 = 1

=> 7x + 8y = 56

The equation of the required line is 7x + 8y = 56

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