Nine Grade Math Slope

Introduction to nine-grade math slope:

Nine- grade math slope article deals with how to find the slope from the slope intercept from of the equation and from the two given points of the line. It includes the slope of the parallel and perpendicular line. We have the different formula to find the slope of the given line

Is this topic How to Construct a Perpendicular Bisector hard for you? Watch out for my coming posts.

Formula related to nine grade math slope.

When two coordinate points on the line is given

Formula to find slope, m = `((y2-y1)/(x2-x1))`

When slope intercept form is given

The slope intercept form is y = mx+b

m = `((y-b)/x)`

Where m is the slope of the line

b is the y intercept.

When two lines are parallel to each other, the slope of the both lines is equal.

When two lines are perpendicular to each other, the product of slope is -1[ (m1*m2)= -1]

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Model problems for nine grade math slope


Example problems for nine grade math

Find the slope of the line whose coordinate points are (2, 3) and (4, 5).


Solution:

(x1,y1) = (2, 3)

(x2,y2) = (4, 5)

Formula:

Formula to find slope, m = `((y2-y1)/(x2-x1))`

= `((5-3)/ (4-2))`

= `(2/2)`

= 1

The slope of the line is 1

2.find the slope of the line whose slope intercept form is 3y = 6x +9

Solution:

The slope intercept form is y= mx+b

The given equation is 3y= 6x +9
rewrite the equation of the line

y= `(6/3)x+(9/3)`

y= 2x+3

Now it is in the standard form.

Therefore, the slope of the line is 2

3. Line AB and CD are perpendicular to each other, find the slope of the line CD when the two points on the lineAB is (2, 7) and (6, 4)

Solution:

(x1,y1) = (2, 7)

(x2,y2) = (6, 4)

Formula:

Formula to find slope, m = `((y2-y1)/(x2-x1))`

= `((4-7)/(6-2))`

= `((-3)/4)`

= `(-3/4)`

The slope of the line is `(-3/4)`

Since AB and CD are perpendicular to each other.

so, the slope of the CD =` (- 1/"slope of AB")`

= `(-1/ ((-3/4)))`

= `(4/3)`

Slope of the line CD is `(4/3)`

Learn Online Perpendicular

Introduction to learn online perpendicular lines:

Perpendicular means nothing but when two lines are cross in either direction and form right or 90 degree angles, so a horizontal line  and a vertical line  that cross are perpendicular because they form right angles.
Perpendicular lines are two lines which meet at a right angle. Right angle is 90degrees. Please express your views of this topic Slope of a Perpendicular Line by commenting on blog.


Learn perpendicular lines online through examples


1)Find the equation of the perpendicular line  to y = `(1)/(2)` x-5, passing through the point (4, 10).

Learn perpendicular lines online by using slope-intercept form:

Since the original line has a slope of `(1)/(2)`  , a perpendicular line must have a slope of -2.

Therefore, the equation must look like y = -2x + b.

Substituting the given point in place of x and y we have: 10 = -2(4) + b. Solving, we find that b = 18.

The equation is y = -2x + 18.

Learn perpendicualr lines online by using point-slope form:

Again, the perpendicular slope is m = -2. The equation must look like y - y1= -2(x - x1).

Substituting the given point in place of x1 and y1 we have y - 10 = -2(x - 4).

Rearranging yields y - 10 = -2x + 8 or y = -2x + 18.

2) Show that the lines 6x +3y +9 = 0 and 3x-5y+7 = 0 are perpendicular.

Solution: Given equation of lines as 6x + 3y + 9 = 0 and 3x + 5y+7 = 0

First line:   6x + 3y + 9 = 0                                                Second line:  3x - 5y + 7 = 0

6x + 3y + 9 - 9 = 0 -9                                                              3x - 5y + 7 -7 = 0 -7

6x + 3y = -9                                                                              3x - 5y = -7

6x -6x + 3y = -9 - 5x                                                                3x - 3x - 5y = -7 -3x

3y = -6x - 9                                                                               -5y = -3x-7

3y/3 =  (-6x-9)/3                                                                       5y/5 = (3x+7)/5

y = -5/3x -3                                                                              y =  3/5x +7/5

compare with y = mx + b                                                     compare with y = mx +b

m =`(-5)/(3)` and b = -3                                                              m = `(3)/(5)`  and b = `(7)/(5)`

Condition for lines to be perpendicular is m 1 * m2 = -1

Here, m 1 = `(-5)/(3)`  and  m 2 = `(3)/(5)` ,

m1 * m 2 = `(-5)/(3)` *`(3)/(5)`  =  -1

Therefore the  5x +3y +9 = 0 and 3x-5y+7 = 0 are perpendicular lines.

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learn perpendicular online -formula


Two lines are perpendicular to each other when the product of their slopes is -1

Let slope of first line is m1

Slope of second line is m2

m1 * m2 = -1

Slope of a line between points (x1,y1) and (x2,y2) is     m =`(y_(2)- y_(1))/(x_(2)- x_(1))`

Equation of line in slope intercept form is y = mx +b , where m is the slope of line and b is the y intercept of line

The equation of all lines perpendicular to the line ax +by +c = 0 can be written as bx –ay +k = 0 for different values of k