Answer:
Part 1) The equation in slope intercept form is
Step-by-step explanation:
Part 1) Write an equation in slope-intercept form for a line that passes through (3,4) (and has a y intercept of -8)
we know that
The equation of a line in slope intercept form is equal to
where
m is the slope
b is the y-intercept
we have
substitute
solve for m
therefore
To turn into a fraction you should do such steps:
1 step. Set up an equation by representing the repeating decimal with a variable. Using your example, you will let x represent the repeating decimal 0.(6), so you have x=0.666... .
2 step. Identify how many digits are in the repeating pattern, or n digits. Multiply both sides of the equation from Step 1 by to create a new equation. Again, using your example, you see that the repeating pattern consists of just one digit: 6. Now multiply both sides of the equation by
. Thus, you have
or
.
3 step. Subtract the equation in Step 1 from the equation in Step 2. Notice that when we subtract these equations, our repeating pattern drops off. Therefore, .
4 step. You now have an equation that you can solve for x and simplify as much as possible, using x as a fraction: . If you divide both sides by 9, you get
. When simplified, you get that
.
Answer: .