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.

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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