First we must find the opposite-reciprocal of the original slope.
current slope:
new slope:
Using the new slope and the given point, we will plug them into slope-intercept form and solve for b, the y-intercept.
The y-intercept is .
Now, we can write the formula for the new line.
Slope-intercept form:
Point-slope form:
I would use a chart to solve this problem.
This is a good wya to organize your information.
Down the left side, list the people involved.
I put Bob first and the mom second but the order doesn't matter.
Since Bob's mom is 3 times older than Bob, we can represent
Bob's age now as x and Bob's mom's age now as 3x.
Bob's age in 12 years will be x + 12 and Bob's mom's
age in 12 years will simply be 3x + 12.
Since the second sentence starts with in 12 years,
we will be using the information from our second column.
In 12 years, Bob's mom's age, 3x + 12, will be,
equals, twice of her son's age, 2(x + 12).
Solving from here, we find that x = 12.
This means that Bob's age now is 12 and his mom is 36.
The chart is attached below.
