Graphing Lines - Pre-Algebra

The equation of the line is written in slope-intercept form, , where is the slope and is the y-intercept. In this example, the y-intercept is a negative number.

In the standard form of a line the slope is represented by the variable .

In this case the line has a slope of .

The answer is .

To find the slope of a line with two points you must properly plug the points into the slope equation for two points which is

We must then properly assign the points to the equation as and .

In this case we will make our and our .

Plugging the points into the equation yields

Perform the math to arrive at

The answer is .

The y-intercept is the point at which the line intersects the y-axis.

It does this at .

We plug in for in our equation, , to give us .

Anything multiplied by is , so .

Our coordinates for the y-intercept are .

To find the slope of a line with two points we must properly plug the points into the slope equation:

We must then assign the variables and .

In this case we will plug in for and for .

Plugging the points into the equation yields .

Perform the math to arrive at .

The answer is.

In the standard form equation of a line, , the slope is represented by the variable .

In this case the line has a slope of .

Therefore the answer is .

In the slope-intercept form of a line, , the slope is represented by the variable .

In this case the line

has a slope of .

The answer is .

In the slope-intercept form of a line, , the y-intercept is when the line intersects the y-axis.

It does this at .

So we plug in for in our equation

to give us

Anything multiplied by is so

Our coordinates for the y-intercept are .

Parallel lines have the same slope.

If an equation is in slope-intercept form, , we take the from our equation and set it equal to the slope of our parallel line.

In this case .

The slope of our parallel line is .

The slope of a perpendicular lines has the negative reciprocal of the slope of the original line.

If an equation is in slope-intercept form, , we use the from our equation as our original slope.

In this case

First flip the sign

To find the reciprocal you take the integer and make it a fraction by placing a over it. If it is already a fraction just flip the numerator and denominator.

Do this to make the slope

The slope of the perpendicular line is

.

To find the slope of a line with two points you must properly plug the points into the slope equation for two points which looks like

We must then properly assign the points to the equation as and .

In this case we will make our , and our .

Plugging the points into the equation yields

Perform the math to arrive at

The answer is .

To find the slope of a line with two points you must properly plug the points into the slope equation for two points which looks like

We must then properly assign the points to the equation as and .

In this case we will make our and our .

Plugging the points into the equation yields

Perform the math to arrive at

The answer is .

It is known that parallel lines have the same slope and therefore a line that is parallel to:

MUST have the same slope of .

You know that point-slope form is:

and therefore you must look at the slope of your equation given which is .

From there you just plug in what is given:

for ,

for ,

and for

The slope-intercept form of a line is .

To be able to identify the slope of a line, we need to get it in the form of

.

To do this we need to change the coefficient of y to be instead of . To do this, divide both sides of the equation by .

Now we can tell what the value of m, or the slope, is:

The slope of the line is determined by . In other words, we can use the formula .

Let's choose the coordinate to be ( , ) and to be ( , ).

We can now use the formula above:

The formula to calculate slope between two points in a line is , for points and .

If we pick as our and as our , then:

This simplifies to , which can be reduced to

The slope intercept formula is: