Question

Find the inverse function in slope-intercept form for (mx + b).

Option 1: y = -mx - b
Option 2: y = mx + b
Option 3: y = x/m - b
Option 4: y = -x/m + b

Answer 1

The inverse function of y = mx + b in slope-intercept form is obtained by swapping 'x' and 'y', and then solving for 'y'.

Step-by-step explanation:

To find the inverse function of y = mx + b in slope-intercept form, we need to solve for 'x' in terms of 'y', effectively swapping the roles of 'x' and 'y'. The slope-intercept form of a linear equation is commonly written as y = mx + b, where 'm' represents the slope of the line and 'b' is the y-intercept, which is the y-coordinate where the line crosses the y-axis. To find the inverse, we take the following steps:

1. Swap 'x' and 'y' in the original equation, so it becomes 'x = my + b'.
2. Solve for 'y' by first subtracting 'b' from both sides of the equation, which results in 'x - b = my'.
3. Lastly, divide both sides by 'm' to isolate 'y', giving us 'y = (x - b) / m' or 'y = x/m - b'.

Therefore, the correct inverse function in slope-intercept form is Option 4: y = -x/m + b.