# What is the equation of a line that has an x-intercept of (6,0) and a y-intercept of (0,5)?

justaguide | College Teacher | (Level 2) Distinguished Educator

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The x-intercept of the line is (6,0) and the y-intercept of the line is (0,5)

A line with x intercept a and y intercept b can be written in the intercept-intercept form as `x/a + y/b = 1`

Here a = 6 and b = 5

=> `x/6 + y/5 = 1`

=> 5x + 6y = 30

The equation of the required line is 5x + 6y = 30

wisejargon | College Teacher | (Level 1) eNoter

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Let X1, Y1 = (6,0)

Let X2, Y2 = (1,5)

First, let's review the equation of a line:

Y = mX + b where:

m = slope of the line and

b = the Y intercept

X, Y = any given set of X and Y values (such as 6,0 or 1,5).

m = (y1 - y2)/(x1 - x2)

Let's substitute values:

m = (0 - 5)/6 - 1)

m = -5/5

m = -1

Now, let's substitute the value of -1 for "m" and then enter the coordinates of X and Y to find the Y intercept, b:

Y = (-1)X + b

0 = (-1)6 + b

0 = -6 + b

0 + 6 = -6 +6 + b

6 = 0 + b

6 = b

Try substituting the coordinate (1,5) to discover that you'll get b = 6 for the other coordinate.

Therefore, the equation that for this line is:  Y = -1(X) + 6