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slope of a straight line

Slope of a line

Process to find the slope of a line:

• We can take any two point on a line.
• Find the vertical change or change in y coordinate.
• Find the horizontal change or change in x coordinate.
• Find the ratio of these changes i.e. m = rise/run

Slope = change in coordinate y / change in x coordinate

We have basically 4 types of slopes. These are:

Zero Slope: In this case the line is parallel to the x axis, The value of x is change or increased, the value of y remains constant or unchanged.
Positive Slope: In this case as the values of x increase, the value of y is also increased and the slope of a line is positive.
Negative Slope: In this case as the values of x increase, the value of y is decreased and the slope of a line is negative.
No slope: In this case the line is parallel to the y axis, The value of y is change or increased, the value of x remains constant or unchanged.

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orthocenter of a triangle

Orthocenter of a Triangle ABC

 

How to Find the orthocenter of a Triangle 

The orthocenter of a triangle is where all of the altitudes of a triangle meet each other.

The altitude is a perpendicular line segment from a vertex of a triangle to the opposite side (Vertex A to side BC).

To draw the orthocenter, first You draw the triangle on a coordinate plane and draw all three altitudes (one from each vertex of the triangle) and determine the point at which they all intersect. This intersection is a orthocenter of a Triangle ABC.

step by step solution substitution method

Substitution Method

 

Calculate value of x and y: Equations are y-x = 3 and 2(x + y) = 14


Solution:
In substitution method, we have a given equation of two variables, x and y.
First, divide in second equation by 2 in both sides.
x + y = 4 …. (1)
y – x = 3 => y = x + 3 ….(2)
Now, put the value of y in equation 1 and solve the equation for x, i.e
x + (x + 3) = 4
x + x + 3 = 4
2x = 4 –3
which gives x = 1/2.

Now, substitute x = 1/2 in any one of the given equation and find the value of y
y = 1/2 + 3
y = 7/2
Answer is : x = 1/2, y = 7/2

Solving Linear Equation of One Variable Watch Video

Solving Linear Equation of One Variable - Math Watch Video

 

Solve for X:
2/3 X + 1 = X/6 x 3

Answer:
In given equation, we find the value of X.

We see that, the denominator of the given equation is 6, so we just multiplied the whole equation by 6.
6 (2/3 X + 1) = 6(X/6 x 3)

Using the distributive law, we have
4X + 6 = 3X

Now taken out the common terms in single side
4X –3X = –6

which gives
X = –6
Answer is : x = –6

Substitution Method Algebra Watch Video

Solving Linear Equation by Substitution Method Algebra Watch Video

 

Q.
4x + 3y = 1 and x = 1 – y
Solution:
In substitution method, we have a given equation of two variables, x and y.
First you put the value of x in other given equation 4x = 2x + 3y and calculate the value of y.
Steps are:
x = 1 –y
Plug ‘x’ in first equation.
4(1 –y) + 3y = 1
Solve this equation for y
4 –4y + 3y = 1
4 –y = 1
y = 3
Substitute y = 1 in any one of the given equation and find the value of other variable
x = 1 –y
x = 1 –3 = –2
Answer is : x = –2, y = 3

Free Algebra Help Tutorials

Algebra Math Problems

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Linear programming problem standard form

For developing a general method of solution of a linear programming problem, we used the standard form. The basics of standard form is 

1. Non Negativity Constraints i.e. all the constraints are transformed into equations using the addition and substitution of new non negative constraints and change the equation into standard form. These new varaibles are called as slack or surplus variables and are added if <= sign in constraints and subtract if >= in the constraints.  

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