4/6/2022

V Slope Methode

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Algebra -> Linear-equations-> Lesson Point Slope form vs. Slope Intercept form Log On

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V Slope Method Definition

V slope method

This Lesson (Point Slope form vs. Slope Intercept form) was created by by tutoringisfun(17) : View Source, Show
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Point Slope form vs. Slope Intercept form


This lesson will aid students in understanding how to convert from Point Slope form to the more familiar Slope Intercept form.
A linear equation is not always written in the slope intercept form, sometimes it is not even given. Sometimes there is only a point and the slope given. In these instances,
it is necessary to use the point slope formula to obtain the slope intercept formula, so one can solve the equation.
These two formulas are shown below:
y = mx + B - Slope intercept form
(y - Y1) = m(x - X1) - Point Slope form

Example 1

Write the slope intercept form for the following equation using the given slope and point: slope = 12, point ( 3,1).
Here are the steps to get the equation for this line:
1. write down the correct formula
(y-Y1) = m(x-X1)
2. substitute in the values for X1=3, m=12 and Y1=1
(y-1) = 12(x-3)
3. distribute the 12 and get rid of the parenthesis
y-1 = 12x-36
4. solve for y by adding +1 to each side making the 1's on the left cancel out
y-1+1 = 12x-36+1
5. combine like terms and watch your signs.
y = 12x-35.
This is the equation of the line in slope intercept form.

Example 2

Sometimes you might need to determine if two lines are parallel or perpendicular. You can use the point slope formula to figure that out as well.
Write the slope intercept form of the line equation for the line that passes through the point (3,4) and is perpendicular to y = 3x+2.
1. write the point slope formula
(y-Y1) = m(x-X1)
2. substitute in the values from the problem for m, X1=3, Y1=4
(y-4) = -1/3(x-3)
(Remember that perpendicular lines have slopes that are reciprocals and have opposite signs of each other. So, we use the slope m = -1/3 here)
3. distribute the 1/3 to get rid of the parenthesis
y-4 = -1/3x + (1/3)*3)
4. simplyfy the right side by multiplying 3(1/3). The 3's cancel out leaving
y-4 = 1/3x+1
5. solve for y by adding 4 to each side and making the 4's on the left side cancel out.
y-4+4 = -1/3x+1+4.
This gives
y = -1/3x+5
We can check to see if these lines are perpendicular. Indeed, 1/3 is the reciprocal for 3 and -1/3 has the opposite sign, so the lines are perpendicular.

Example 3

Find the equation of the line that is parallel to y = - 6x-2 and goes through the point (1,4).
1. write the point slope formula
(y-Y1 ) = m(x-X1)
2. determine the slope of the parallel line. Parallel lines have the same slope, therefore the slope of the new line is -6
3. substitute the values above for m, Y1=4, X1=1 into the formula
(y-4) = -6(x-1)
4. distribute the 6 and get rid of the parenthesis, watch your signs.
y-4 = -6x+1
5. to solve for y, we add 4 to each side and cancel out the 4's on the left
y-4+4 = -6x+1-4
6. combine like terms
y = -6x-3
7. Look at the slope of the new line to determine if it is the same as the given line
-6 = -6, therefore, the lines are parallel.
I hope this lesson has been useful. If you need more paid help you can contact me through the websites listed on my profile and I will be happy to assist you. Have a great day!
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V Slope Method

V slope method excel