A line on a coordinate plane contains the points (0, 6) and (3, 9). Write the equation of the line in slope intercept form.
Slope intercept form is y = mx + b. m represents the slope of the line or rise/run. This is the ratio of the change in the y value/ the change in the x value from one point to the other. b represents the y-intercept or where the line crosses the vertical y-axis (The value of y when x = 0). x and y in the equation represent the values of the coordinates on the line. We start by finding the slope: change in y is 9-6=3. Change in x is 3-0=3. The ratio of change in y over change in x is 3/3 = 1. Our slope, or m, is 1. To find b we need to use the slope we solved for and plug it into our slope intercept form equation with one of our coordinate values for x and y (They must be from the same point). I will use the first point, but you can use either. y = mx + b (0,6) and m=1 6 = 1(0) + b Solve for b: 6 = 0 + b. b = 6. Write our equation in slope intercept form using our solved values for m and b. y = 1x + 6 or y = x + 6
1/4 + 2/3 - 1/6 = ?
First, we need to find the common denominator by making fractions that are equivalent to each of our original fractions. What common multiple do 4, 3, and 6 (the denominators) have? 4: 4, 8, 12 3: 3, 6, 9, 12 6: 6, 12 They all have 12 as a common multiple, so we will use this as our new denominator to make equivalent fractions. 1/4 = 3/12 (We would need to multiply 4 by 3 to get to our common denominator of 12, so we multiply the numerator by 3 as well. 1 x 3 = 3.) 2/3 = 8/12 (Multiply numerator and denominator both by 4.) 1/6 = 2/12 (Multiply both by 2.) New problem: 3/12 + 8/12 - 2/12 = 9/12. When our denominators are all the same, we just need to add or subtract the numerators from left to right. Our answer is 9/12, but this is not in simplest form. Both numerator and denominator have a common factor of 3 that we can divide out. 9/12 = 3/4. Our answer in simplest form is 3/4.
There are cookies out on a dessert table at a party. John ate some of the cookies. Mary ate four times as many cookies as John, and Bob ate half as many cookies as Mary. If 14 cookies were eaten in total, how many cookies did each person eat?
The number of cookies that John ate will be represented as x. Mary ate four times the number that John ate, so her number will be represented as 4x. Bob ate half the amount of Mary, so his number will be represented as 2x (2 is half of 4). All of the cookies they ate total 14 --> x + 4x + 2x = 14 Add all like terms (have the same variable to the same power; in this case "x") 7x = 14 Solve for x, divide both sides by 7. x = 2 Since John's number is represented by x, and x = 2, John ate 2 cookies. Mary ate 4x or 4(2) = 8 cookies Bob ate 2x or 2(2) = 4 cookies. Check answer: 2 + 8 + 4 = 14 cookies eaten