(Per.1)+Slope,+Slope+of+Parallel+Lines,+Slope+of+Perpendicular+Lines

Slope, Slopes of Parallel Lines, Slopes of Perpendicular Lines. Period 1. Elena Spaulding, Cricket Martin, Erin Sheehy. Formulas by Elena Spaulding Slope: m= __y____2____-y____1__ x 2 -x 1

Example: Given the two points (4,3) and (1,2), find the slope. m= __y____2____-y____1__ x 2 -x 1 m= __3-2__ 4-1 m= __1__ 3

Slope- Intercept Equation: y= mx+ b

Point- Slope Equation: (y-y 1 ) = m(x-x 1 ) Example: The point is (-1,1) and the slope is 2. (y-y 1 ) = m(x-x 1 ) (y-1) = 2(x-(-1)) (y-1) = 2x + 2 y-1 = 2x + 2 Answer: y = 2x + 3



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Cricket Martin

Formulas for slope and questions by Erin Sheehy

The ** slope **of a line is a measure of ** "how steep" ** a line is. The ** slope **of a line can be **positive, negative, zero, and undefined.** Now that we know the different types of slopes let's recall how to calculate the slope of a line if we know two points that the line passes through. for the most part we use the condensed formula or || Let's look at an example || Don't be fooled if the coordinates are given to you as intercepts, as the next example will demonstrate.
 * **Slope Formula**
 * **Ex.1**
 * **Ex. 2** Find the slope of the line having an x intercept of 3 and a y intercept of 4
 * Solution:** The x and y intercepts are really the points (3,0) and (0,4). Therefore we use these points in the formula

Therefore our equation becomes

and our final answer is || Now it is your turn to try. || is below Now what if you are given a linear equation and asked to find the slope. Do you remember how to do that? If you don't remember continue reading! To find the slope of a linear equation, one must put the equation in slope intercept form. Give it a try.
 * **Your Turn #1** Find the slope of the line passing through the points (4,-6) and (-3,7).
 * **Your Turn #2** Find the slope of the linear equation

|| is below Now that we know how to find the slope of a linear equation we are going to learn how to create a linear equation. To create a linear equation we need two things: 1. the slope of the line 2. a point the line passes through || Once we have the above requirements we can substitute them into the **point slope formula** to find the equation.
 * ** Requirements to Create a Linear Equation **


 * **Ex. 3** Find the equation of the line with a slope of 5 and passing through the point (-3,8).
 * Solution:** Since we already have our two requirements to create a linear equation, we simply plug in our information into the point slope formula.

Simplifying we get,

Distributing we get,

Our answer in slope intercept form is

In standard form our answer would be

**Note:** For our class standard form is considered to be

where A,B,C are any real number. || Sometimes we are not directly given the requirements needed to find the equation of a line. Ckeck out example 4.
 * **Ex. 4** Find the equation of a line passing through the points (2,7) and (-3,6). Write the equation in standard form.
 * Solution:** We have one of our requirements, that being a point the line passes through. What we need to find is our slope. Using our slope formula we can get





Now that we have our slope we can use either given point to create our linear equation. Let's use the point (2,7).





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