Summarize the following:
Point-slope form allows you to write the equation of a line when you know its slope and have an (x, y) coordinate. You would use this formula when you want to define a second parallel line to an already given line with a defined slope. The formula is y y1= m(x x1) where m is the slope of the line, x1 is the x coordinate of a point given on the line and y1 is the y coordinate of that point. As in the slope-intercept equation, x and y are variables that represent coordinates on the line; generally, you will see them remain as x and y in the equation. The following steps will work through this example: Write the equation of a line parallel to the line y = -4x + 3 that goes through point (1, -2). When writing the equation of a new line, you must first identify the slope of the line you want to draw yours parallel to. Make sure the equation of the original line is in slope-intercept form and then you know the slope (m). The line we want to draw parallel to is y = -4x + 3. In this equation, -4 represents the variable m and therefore, is the slope of the line. This equation only works if you have a coordinate that passes through the new line. Make sure you don't choose a coordinate that is on the original line. If your final equations have the same y-intercept, they are not parallel, but the same line. In our example, we will use the coordinate (1, -2). Remember the formula is y y1= m(x x1). Plug in the slope and coordinates of your point to write the equation of your new line that is parallel to the first. Using our example with slope (m) -4 and (x, y) coordinate (1, -2): y (-2) = -4(x 1) After you have plugged in the numbers, the equation can be simplified into the more common slope-intercept form. This equation's line, if graphed on a coordinate plane, would be parallel to the given equation. For example: y (-2) = -4(x 1) Two negatives make a positive: y + 2 = -4(x -1) Distribute the -4 to x and -1: y + 2 = -4x + 4. Subtract -2 from both side: y + 2 2 = -4x + 4 2 Simplified equation: y = -4x + 2

summary: Define the point-slope equation. Determine the slope of the first line. Identify a point on the new line. Write the equation of the new line with the point-slope form. Simplify the equation.

Summarize the following:
A television is originally priced at $154.88. It now has a 40% discount. Convert the percentage discount to a decimal by moving the decimal two places to the left: 40%=40.0%=.40{\displaystyle 40\%=40.0\%=.40}. Multiply the original price by the decimal: 154.88.40=61.95{\displaystyle 154.88 imes .40=61.95}. Subtract the discount from the original price: 154.8861.95=92.93{\displaystyle 154.88-61.95=92.93}. So, the sale price of the television is $92.93. The original price is $449.95. Convert the percentage discount to a decimal by moving the decimal two places to the left: 15%=15.0%=.15{\displaystyle 15\%=15.0\%=.15}. Multiply the original price by the decimal: 449.95.15=67.49{\displaystyle 449.95 imes .15=67.49}. Subtract the discount from the original price: 449.9567.49=382.46{\displaystyle 449.95-67.49=382.46}. So, the sale price of the camera is $382.46. A tablet is regularly $199.99. On sale, it is 45% off. Round the original price to the nearest ten. Since $199.99 is only 1 cent away from $200, you would round up. Calculate 10% of the rounded price. Moving the decimal one place to the left, you should see that 10% of $200.00 is $20.00. Determine the number of tens in the percent off. Since 104=40{\displaystyle 10 imes 4=40}, you know that there are 4 tens in 45%. Multiply 10% of the rounded price by the appropriate factor. Since the percentage off is 45%, you would multiply 10% of the rounded price by 4: $204=$80{\displaystyle \$20 imes 4=\$80} Calculate 5% of the rounded price. This is half of 10%, which is $20. So half of $20 is $10. Add the remaining 5% to the discount. 40% is $80, and 5% is $10, so 45% is $90. Subtract the discount from the rounded price: $200$90=$110{\displaystyle \$200-\$90=\$110}. So the estimated sale price is $110.

summary: Calculate the exact sale price. Find the exact sale price of a camera that is 15% off. Estimate the sale price.

Summarize the following:
Let's say we're working with the problem 3/4. Simply write a "4" outside the division bar with a "3" on the inside. The "4" is your divisor, and the "3" is your dividend. Since you're working with a fraction, you know that your answer will be less than one, so this first step is necessary. After you do this, you'll need to place a decimal after the 3 under the division bracket and write an additional zero after it. Though 3 and "3.0" are the same, adding the extra zero will allow you to divide 4 into the 3.0. . When you do long division, you can pretend that the decimal points don't exist and act like you're just dividing 4 into 30, for now. Here is how you do it: First, divide "4" into 3.0, which you can think of as 30. The closest you can get is 4 x 7, or 28, which will give you a remainder of 2. So, write a 7 after the "0." above the division bracket and "28" below the "3.0" under the division bracket. Under that, write 2, your remainder, or what you have left when you subtract 28 from 30. Next, add another "0" to the "3.0" so you have "3.00", or what you can think of as "300," under the division bracket. This will allow you to drop down another 0 to the right of the "2" so you can divide "4" into "20." Divide "4" into "20" to get 5. Write the "5" to the right of the "0.7" above the division bracket, so you have "0.75" written there. You'll find that "3" divided by "4" will give you ".75". Write down this answer and you're all done.
summary: Write the denominator outside the division bracket and the numerator inside of it. Place a zero with a decimal point after it above the division bracket. Use long division to get your answer Write your answer.