A line whose y-intercept is 1 less than its x-intercept forms with the coordinates axes a triangle of area 6 square units what is its equation?

Answer 1

-5

Answer 2

This line will form a triangle with base x ( which is also the x-intercept) and height y (which is also the y-intercept). Since the y- intercept is 1 less than x- intercepts, we can say that height is x -1.

Since the area of a triangle is equal to one half of the product of base and height, we can say that area of the triangle is equal to:

(1/2)(x)(x-1) = 6

(1/2)x2 - 1/2x = 6 multiply by 2 to both sides;

x2 - x = 12 add 1/4 to both sides to complete the square;

x2 - x + 1/4 = 12 + 1/4 use the formula (a - b)2 = a2 - 2ab + b2

(x - 1/2)2 = 49/4 since the distance is positive, use positive root;

x - 1/2 = 7/2 add 1/2 to both sides

x = 8/2 = 4 which gives us the point (4, 0)

y = x - 1

y = 4 - 1 = 3 which gives us the point (0, 3)

Now we have a point on the line that we can use to find the equation of the line. This point is (4, 0), and two points on the line to find the slope. So,

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

m = [(3 - 0] /(0 - 4)

m = -3/4

(y - y1) = m(x - x1)

(y - 0) = -3/4(x - 4)

y = -3/4x + 3 which is the equation of the line, or in the general form;

3/4x +y - 3 = 0