Find the equation of a line through (1,3) and forming with the axes a triangle of area 6 square units. (Give three solutions).

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Graph the situation. Place a point at (1,3). Notice the slope needs to be negative (in order to make a triangle with the axes). Now explore various y-intercepts.

For example: A y-intercept of 4 yields a slope of -1, but the area of this triangle is 1/2 (4*4) which is...

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Graph the situation. Place a point at (1,3). Notice the slope needs to be negative (in order to make a triangle with the axes). Now explore various y-intercepts.

For example: A y-intercept of 4 yields a slope of -1, but the area of this triangle is 1/2 (4*4) which is 8 not six. Check out y-intercept of 5.

Now look at y-intercept of 6 : this yields a slope of -3 and cross the x-axis at 2. So the area is 1/2(2*6) which is 6. So the line has slope of -3 and y-intercept of 6 => y = -3x + 6.

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