## Properties of a straight line

### Rearrange:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

6*x-2*y-(2)=0

### Step 1 :

#### Pulling out like terms :

Pull out like factors :

6x - 2y - 2 = 2 • (3x - y - 1)

#### Equation at the end of step 1 :

### Step 2 :

#### Equations which are never true :

Solve : 2 = 0

This equation has no solution.

A a non-zero constant never equals zero.

#### Equation of a Straight Line

Solve 3x-y-1 = 0

Tiger recognizes that we have here an equation of a straight line. Such an equation is usually written y=mx+b ("y=mx+c" in the UK).

"y=mx+b" is the formula of a straight line drawn on Cartesian coordinate system in which "y" is the vertical axis and "x" the horizontal axis.

In this formula :

y tells us how far up the line goes

x tells us how far along

m is the Slope or Gradient i.e. how steep the line is

b is the Y-intercept i.e. where the line crosses the Y axis

The X and Y intercepts and the Slope are called the line properties. We shall now graph the line 3x-y-1 = 0 and calculate its properties

#### Graph of a Straight Line :

#### Calculate the Y-Intercept :

Notice that when x = 0 the value of y is 1/-1 so this line "cuts" the y axis at y=

y-intercept = 1/-1 =#### Calculate the X-Intercept :

When y = 0 the value of x is 1/3 Our line therefore "cuts" the x axis at x=

x-intercept = 1/3 =#### Calculate the Slope :

Slope is defined as the change in y divided by the change in x. We note that for x=0, the value of y is and for x=, the value of y is So, for a change of in x (The change in x is sometimes referred to as "RUN") we get a change of - () = in y. (The change in y is sometimes referred to as "RISE" and the Slope is m = RISE / RUN)

Slope = 3### Geometric figure: Straight Line

- Slope = 3
- x-intercept = 1/3 =
- y-intercept = 1/-1 =

Here we will show you how to calculate and provide solutions to math problems related to 6x - 2y = 2.

We will start by calculating and showing you the solution for the x-intercept and y-intercept of 6x - 2y = 2.

Then, we will show you how to get the graph plot coordinates for 6x - 2y = 2 so we can illustrate it on a graph.

Finally, we will solve 6x - 2y = 2 for x and also for y, then calculate and show you the solution for the slope of 6x - 2y = 2.

**Find x-intercept**

The x-intercept is where the graph crosses the x-axis. To find the x-intercept, we set y

_{1}=0 and then solve for x.

6x - 2y = 2

6x - 2(0) = 2

**x**

_{1}=**y**

_{1}= 0**Find y-intercept**

The y-intercept is where the graph crosses the y-axis. To find the y-intercept, we set x

_{2}=0 and then solve for y.

6x - 2y = 2

6(0) - 2y = 2

**y**

_{2}= -1**x**

_{2}= 0**Get Graph Plot Coordinates**

Getting two graph points will allow you to make a straight line on a graph. The plot coordinate format is (x

_{1},y

_{1}) and (x

_{2},y

_{2}).

Thus, we use the x-intercept and y-intercept results above to get the graph plots for 6x - 2y = 2 as follows:

(x

_{1},y

_{1}) and (x

_{2},y

_{2})

**(,0)**and

**(0,-1)**

**Solve for x**

To solve for x, we solve the equation so the variable x is by itself on the left side:

6x - 2y = 2

**x = y +**

**Solve for y**

To solve for y, we solve the equation so the variable y is by itself on the left side:

6x - 2y = 2

**y = 3x - 1**

**Find slope**

The slope of the line (m) is the steepness of the line. It is the change in the y coordinate divided by the corresponding change in the x coordinate. Simply plug in the coordinates from above and solve for m to get the slope for 6x - 2y = 2

m = (y

_{2}- y

_{1})/(x

_{2}- x

_{1})

m = (-1 - 0)/(0 - )

**m =**

**Ax - By = C Calculator**

Now you know how to solve 6x - 2y = 2. Enter another math problem here:

**6x - 2y = 3**

Here is the next algebra problem on our list. Check it out!

Answers are rounded to the nearest thousandth if necessary. If you want exact answers instead of rounded answers, then keep the fraction answers when you solve the equations instead of converting them to decimal numbers like we did.

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## The Graph of The Following System of Equations is −2x + y = 3 and 4x + 2y = 2. Solve this using the graph.

An equation of degree 1 is called linear equations. The standard form of linear equations in two variables is ax + by = c, where a, b and c are constants.

### Answer: The solution for the system of linear equations -2x + y = 3 and 4x + 2y = 2 is (x, y) = (, 2)

Let's solve the system of linear equations in two variables.

**Explanation:**

The given equations are -2x + y = 3 (1) and 4x + 2y = 2 (2)

From the graph, it is clear that the intersecting point of the given two linear equations is (, 2). So, this is the solution of the given system of equations.

Let's solve the equations algebraically.

From equation (2), we get

4x + 2y = 2

x = (2 - 2y) / 4

To solve the system of linear equations, we will substitute value of x = (2 - 2y) / 4 in equation (1) and solve for x.

⇒ -2((2 - 2y) / 4) + y = 3

⇒ -4 + 4y + 4y = 12

⇒ 8y = 12 + 4

⇒ 8y = 16

⇒ y = 2

Put y = 1 in equation (2).

⇒ x = (2 - 2(2))/4 = (2 - 4)/4 = -2/4

⇒ x =

We can use Cuemath's online system of equations calculator to solve the equations.

### Thus, the solution for the system of linear equations is (x, y) = (, 2)

**Hint:**To solve this we need to give the values of ‘x’ and we can find the values of ‘y’. Otherwise we can find the coordinate of the given equation lying on the line of x- axis, we can find this by substituting the value of ‘y’ is equal to zero (x-intercept). Similarly we can find the coordinate of the equation lying on the line of y- axis, we can find this by substituting the value of ‘x’ equal to zero (y-intercept).

**Complete step by step solution:**

Given, \[3x + 2y = 2\].

To find the x-intercept. That is the value of ‘x’ at\[y = 0\]. Substituting this in the given equation. We have,

\[3x + 2(0) = 2\]

\[3x = 2\]

Divide by 3 on both sides of the equation,

\[x = \dfrac{2}{3}\]

\[x = \].

Rounding off the decimal number we have,

\[ \Rightarrow x = \]

Thus we have a coordinate of the equation which lies on the line of x-axis. The coordinate is \[(,0)\].

To find the y-intercept. That is the value of ‘y’ at \[x = 0\]. Substituting this in the given equation we have,

\[3(0) + 2y = 2\]

\[2y = 2\].

Divide by 3 on both sides of the equation,

\[y = \dfrac{2}{2}\]

\[ \Rightarrow y = 1\]

Thus we have a coordinate of the equation which lies on the line of the y-axis. The coordinate is \[(0,1)\].

Thus we have the coordinates \[(,0)\] and \[(0,1)\].

Let’s plot a graph for this coordinates,

We take scale

x-axis= 1 unit = units

y-axis= 1 unit = units

All we did was expand the line touching the coordinates \[(,0)\] and \[(0,1)\] by a straight line.

Without calculation we have found out one more coordinate is \[(,),(,)\] and \[(,)\]

**Note:**Intercept method is an easy method for drawing graphs. A graph shows the relation between two variable quantities, it contains two axes perpendicular to each other namely the x-axis and the y-axis. Each variable is measured along one of the axes. In the question, we are given one linear equation containing two variables namely x and y, x is measured along the x-axis and y is measured along the y-axis while tracing the given equations.

## 2y=2 graph

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