Question

Please help me with this question

Answer 1

y = -1/2 x - 1

Explanation:

A (-2,0)

B (0,-1)

slope = (-1-0)/(0-(-2)

-1/2

y intercept = -1

y = -1/2 x - 1

Answer 2

y = e^(-1/2x -1)

Explanation:

You want the equation for y(x), which is graphed as a straight line on a semi-log scale.

Graph

Let z = ln(x). The graph shows a straight line with a z-intercept of -1 and a slope of "rise"/"run" = -1/2. That means the slope-intercept equation for this line can be written as ...

z = -1/2x -1

Equation

Using z = ln(y), we can find the equation for y by taking antilogs:

ln(y) = -1/2x -1

y = e^(-1/2x -1)

__

Additional comment

The attached graph shows y = f(x) and the line ln(y).