A **linear equation** is an algebraic equation in which each term is either a constant or the product of a constant and (the first power of) a single variable. Linear equations can have one or more variables.

**One variable**

A linear equation in one unknown x may always be rewritten ** ax=b** If

**a≠0**, there is a unique solution

**x=b/a**If

**, then either the equation does not have any solution, if**

*a≠0**(it is inconsistent), or every number is a solution, if*

**b≠0***is also zero.*

**b****Two variables**

A common form of a linear equation in the two variables * x* and

*is*

**y***, where*

**y=mx+b***and*

**m***designate constants (parameters). The origin of the name “linear” comes from the fact that the set of solutions of such an equation forms a straight line in the plane. In this particular equation, the constant m determines the slope or gradient of that line, and the constant term*

**b***determines the point at which the line crosses the*

**b***-axis, otherwise known as the*

**y***-intercept.*

**y****General (or standard) form**

In the general (or or standard ) form the linear equation is written as: * Ax+By+C=0* where

*and*

**A***are not both equal to zero. The equation is usually written so that*

**B***, by convention. The graph of the equation is a straight line, and every straight line can be represented by an equation in the above form. If*

**A>0***is nonzero, then the*

**A***-intercept, that is, the x-coordinate of the point where the graph crosses the x-axis (where, y is zero), is*

**x***. If B is nonzero, then the*

**C/A***-intercept, that is the*

**y***-coordinate of the point where the graph crosses the y-axis (where x is zero), is*

**y***, and the slope of the line is*

**C/B***. The general form is sometimes written as:*

**-A/B***where*

**ax+by+c=0***and*

**a***are not both equal to zero. The two versions can be converted from one to the other by moving the constant term to the other side of the equal sign.*

**b****Intercept form**

* x/a+y/b=1*, where

*and*

**a***must be nonzero. The graph of the equation has*

**b***-intercept*

**x***and*

**a***-intercept*

**y***b*. The intercept form is in standard form :

*with*

**Ax+By+C=0***and*

**A/B=1/a***. Lines that pass through the origin or which are horizontal or vertical violate the nonzero condition on a or b and cannot be represented in this form.*

**B/C=1/b****Find The Slope of a Line**

In mathematics, the slope or gradient of a line is a number that describes both the direction and the steepness of the line . Slope is often denoted by the letter m. If the equation of the line is y=mx+b, then m is the slope.

**Questions**

**1)** How to find the slope of a line given 2 points * (-3;5)* ,

*using UMS ?*

**(4;6)***Answer*

The equation of the line is * y=mx+b*,

*is the slope*

**m**First point of the line is

*, or*

**(-3;5)***,*

**x=-3**

**y=5**Second point of the line is

*or*

**(4;6)***,*

**x=4**

**y=6**Enter

Solve using UMS and find **m**

The final answer is **m=1/7**

**2)** How to find the slope of a Line : ** 6x+2y=10** using UMS ?

*Answer*

The equation of the line is * y=mx+b*,

*is the slope*

**m**Enter :

*and solve using UMS for*

**6x+2y=10****.**

*y*We get

**y=-3x+5**The final answer is

**m=-3*** 3)* How to find the slope of a Line

*using UMS ?*

**x/5+3/y=4****Answer**

The equation of the line is * y=mx+b*,

*is the slope.*

**m**Enter

*and solve using UMS for*

**x/5+3/y=4****y**

We get

The final answer is

We get

*therefore***y=-4(x-5)/15****y=-4/15x+20/15**The final answer is

**m=-4/15**

**4)** How to find the slope of a Line : * 3x-7y+5=0* using UMS ?

**Answer**

The equation of the line is * y=mx+b*,

*is the slope.*

**m**Enter :

*and solve using UMS for*

**3x-7y+5=0**

**y**We get

*therefore*

**y=(3x+5)/7**

**y=3/7x+5/7**The final answer is

**m=3/7**