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?

4/5 OR -4/5

Step-by-step 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

it has changed from the width and the height.

step-by-step explanation:

check above link.

graphically?   well, you graph them both, the solutions is where they both intersect each other, since there are two solutions, meaning they will meet twice, or namely the linear will run into the quadratic curve twice, and where they meet, those x,y coordinates are the solutions to the system.