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These two numbers make up an ordered pair; we write an ordered pair using (parentheses).

We can represent a specific location, or point, in a rectangular coordinate system by using two numbers; an x-value and a y-value.

Quadrants are labeled as follows:

I = Right Upper Quadrant

NOTE:

Points that lie on an axis are not considered to be in any quadrant.

3(3) + 2(5) = 19

Is (3, 5) a solution to 3x + 2y = 19?

3(6) = 2(-4) + 10

Is (6, -4) a solution to 3x = 2y + 10?

1.) Substitute a value for one of the variables.

To find a solution to a linear equation in two variables:

x = 1

Find three solutions to 2x + y = 13

You simply choose it ;-)

Where do you find the value for x?

When solving linear equations in two variables that contains a fraction,

choose multiples of the denominator to end up working with integers.

x + y

Making a table of values can help keep the ordered pairs organized.

To graph a linear equation in two variables:

1.) Find three ordered pairs that are solutions to the linear equation.

1.) Let y = 0

Finding the x-intercept of a linear equation:

1.) Let x = 0

Finding the y-intercept of a linear equation:

3x - 6(0) = 12

x = (4, 0) and y = (0, -2)

To graph an equation using the intercepts:

1.) Find the x-intercept by letting y = 0 and solving for x.

Some linear equations only have one intercept.

Most linear equations have one x-intercept and one y-intercept.

Graphing linear equations through the origin

An equation in the form Ax + By = 0, where A and B are not both zero, will pass through the origin and the only intercept will be (0, 0)

m = rise / run

One way that we can describe the slope of a line on a graph is

(x1, y1) (x2, y2)

The rise is found by subtracting y-values

On a graph, the slope measures the steepness of a line

- A line with a positive slope goes up from left to right.

The slope of a horizontal line is 0.

The slope of a vertical line is undefined.

Remember the formula to find slope is

m = y2 - y1 / x2 - x1

y = -6x

1.) Find the y-intercept.

1.) Find the slope and the y-intercept.

Graphinf a linear equation with slope and y-intercept

What if the point given is not the y-intercept?

We can use another form of a linear equation called point-slope form.

1.) Write the point-slope equation y - y1 = m (x - x1)

The point-slope form of an equation of a line whose slope is m and that passes through the point (x1, y1) is given by y - y1 = m (x - x1)

Finding the slope of a line that passes through (x1, y1) and (x2, y2)

1.) Put it into the formula m = y2 - y1 / x2 - x1