Question

Find an equation of the line in the form ax by=c whose x-intercept is 12 and y-intercept is 4, where a, b, and c are integers with no factor common to all three, and greater than or equal 0.

Answer 1

The equation of line whose x-intercepts is 12 and y- intercept is 4 is

3x + y = 36.

According to the given question.

We have a equation of line.

ax + by = c.

Also, x-intercept is 12 and y intercept is 4.

As we know that,the x-intercept for any curve is the value of the x coordinate of the point where the graph cuts the x-axis and y coordinate is zero.

And, the y-intercept is the point where the graph intersects the y-axis and the x-coordinate is zero.

Therefore, we have two points (12, 0) and (0, 4).

So, the equation of line from the two point s(12, 0) and (0, 4) is given by

(  y - 0) = (4 - 0/0 - 12)(x -12)

⇒ y = 4/-12(x -12)

⇒ y = -3(x -12)

⇒ y = -3x + 36

⇒ 3x + y = 36

By comparing the given equation of line ax + by = c with the above equation we get

a = 3, b = 1 and c = 36.

Hnce, the equation of line whose x-intercepts is 12 and y- intercept is 4 is 3x + y = 36.

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