To shift the line left four units, we will need to replace the x-variable with the quantity of:

Replace this term in the original equation.

Use distribution to simplify.

The answer is:  

Rewrite this equation in slope-intercept form, .

Shifting this equation up one unit will add one to the y-intercept.

The equation becomes:  

To shift this equation left three units, we will need to replace the x-variable with the quantity .

Use distribution to simplify the equation.

The answer is:  

If the line is shifted right 5 units, we will need to replace the x-variable of the equation with the quantity .

Simplify by distribution.

The answer is:  

Before we apply any transformations, we will need to put the equation in slope-intercept form, .

Subtract  from both sides.

Divide by nine on both sides.

Shifting the equation up two units will add 2, or  to the y-intercept.

The answer is:  

To shift the line left 8 units, we will need to replace the x-value with .

Distribute the negative four through the binomial.

Combine like-terms.  

The answer is:  

To shift the equation left eight units, replace the x-variable with the quantity of .

Simplify this equation.

Combine like-terms.

The answer is:  

Rewrite the given line in standard form to slope-intercept format:

Subtract  on both sides.

Replace the x-value with the quantity of  since we are shifting the equation left 9 units.

Distribute the negative sign through both terms of the binomial.

The answer is:  

Use distribution to simplify the equation.

The equation in slope-intercept form is:  

Shift the equation down six units means subtract the y-intercept by six.

The answer is:  

Use the given function  to find the linear transformation defined by .  

First understand that in order to write  we have to take our function  and evaluate it for  and then add  to the result. 

Adding , 

Now that we have , compute the inverse . Conventionally we replace the  notation with the  notation and solve for 

Therefore, 

At this point it's conventional to interchange  and  to write the inverse since we want to express it as a function of 

Therefore the slope is  and the y-intercept is 

In order to take an action from standard form to slope-intercept form you want to make it of the form:

where  is the y-intercept (constant/number without a variable attached to it)

 is the slope and coefficient of the  term

and the equation is set equal to  making it easier to plot graphically.

Given:

I. Isolate  on one side of the equation. This is done by shifting either  over to the other side of equation or the  term and the constant to the other side of the equation. It is generally preferable to shift it to make so the  term is positive by itself to simply operations and sign mixups. So in this case both  and  would be subtracted from both sides of the equation leaving:

II. Now that  is isolated by itself you want to simplify the equation so there is no coefficient other than  attached to , so in this case it'd mean dividing both sides by   leaving:

III. Simplify the expression. If you are given fractions that are divisible by each other they can be simplified.

In the case   is simplified to  and   is simplified to  leaving the final answer of: