Question

The $x$-intercept of a positively-sloped line is -5, and the area of the triangle formed by the line, the $x$-axis, and the $y$-axis is 10. What is the slope of the line?

Answer 1

4/5 OR -4/5

Explanation:

So, area of triangle = 1/2 * base * height

base = 5 (because x-axis is base, x-intercept is -5, so x-length = 5)

height is unknown

area = 10

We can form the equation: 1/2 * 5 * height = 10

Rearrange terms to get: height (y-height) = 10 / (0.5 * 5) = 4

Following the formula for gradient, dif in y / dif in x, we get 4/5

Therefore our gradient is (4/5), or 0.8.

But because we are only told the x-intercept, it can cross the y axis at y = 4 or y = -4. So there are actually 2 possible gradients, 4/5 and -4/5