find the slope for the graph of the equation

Before we know how to find the slope for the graph of the equation ,lets see what is slope.

Slope is used to describe the steepness, incline, gradient, or grade of a straight line. A higher slope value indicates a steeper incline. The slope is defined as the ratio of the "rise" divided by the "run" between two points on a line, or in other words, the ratio of the altitude change to the horizontal distance between any two points on the line. It is also always the same thing as how many rises in one run.

Using calculus, one can calculate the slope of the tangent to a curve at a point.

The concept of slope, and much of this article, applies directly to grades or gradients in geography and civil engineering.

Question:-

Draw the graph of 2x-3y=12. Use the graph to find the slope of line and area between the axes.

Answer:-

This Online help with math shows us ,how to draw the graph for the above problem.

by simplifying the equation we get.

y=0, x=6
y=-2, x=3
y=-4, x=0

We also use the slope formula to get the slope on the line .

A problem on pythogoras theorm

In any right triangle, the area of the square whose side is the hypotenuse (the side opposite the right angle) is equal to the sum of the areas of the squares whose sides are the two legs (the two sides that meet at a right angle).

The theorem can be written as an equation:

where c represents the length of the hypotenuse, and a and b represent the lengths of the other two sides.



Question:-

Calculate the value of cos θ in the above triangle.

Solution:-

Use Pythagoras theorem to evaluate the length of PR.

PR=√122+202

       adjacent
Cosθ= ----------
       hypotenuse

   RQ
= ----
   PR

    12
 = -----
   √544


 = 0.514 is the Answer

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How to find the factors for an equation

Topic:-Factors of an equation

what is factorization : the decomposition of an object a product of other objects, or factors, which when multiplied together give the original. For example, the number 15 factors into prime factors as 3 × 5, and the polynomial x² − 4 factors as (x − 2)(x + 2). In all cases, a product of simpler objects is obtained. However, factors are not needed to divide evenly because they are still divisible by any number. For example, technically 3 and 8/3 are factors of 8. But, when factoring for tests teachers are looking for the even divisibility of the numbers.
Let's look an example on it.

Question:-

Solve x²+16x+69=6

Answer:-
x²+16x+69=6

x²+16x+69-6=0

x²+16x+63=0

For factoring it ,we find two factors of 63
which add up to 16,they are 9 and 7

x²+9x+7x+69=6

Pair these terms

x(x+9)+7(x+9)=0

(x+9)(x+7)=0

x+9=0 0r x+7=0

x= -9 or x= -7

So x= -9 or -7 is the answer.

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