Vertical shifts will change the y-intercept.  Shifting the equation up two units will add two to the y-intercept.

The equation becomes:  

Shifting the equation left three units means that the inner term  will become .

Replace the term.

The equation becomes:  

Simplify this equation by distribution.

The answer is:  

Rewrite the given standard form equation in slope-intercept format: 

Subtract  from both sides.

Divide by two on both sides.

Simplify both sides.

If this equation is shifted left two units, the  will be replaced with .

Rewrite the equation and simplify.

The answer is:  

Simplify the equation given by distributing the integer through the binomial and combine like-terms.  This will put the equation in slope intercept form.

Since this equation is shifted left four units, replace  with .

Simplify this equation.

The new equation after the shift is:  

Rewrite the given equation, , in standard form to slope intercept form, .

Subtract  from both sides. 

Divide by two on both sides.

Simplify the equation.

The vertical shift by four units will shift the y-intercept up four units.  Add four to the equation.

The answer is:  

The equation given is currently in standard form.

Rewrite the equation in slope-intercept form, .

Subtract  on both sides of .

Divide by two on both sides.

Simplify the fractions and split the right fraction into two parts.

The equation in slope-intercept form is:  

Apply the translation.  If this line is shifted up two units, the y-intercept will be added two.

The answer is:  

Rewrite the given equation  in standard form to slope-intercept form, .

Add  and subtract three on both sides.

Simplify both sides.

Since the line is shifted three units to the right, the  term will become .

Replace this with the variable in the equation.

Simplify.

The answer is:  

Shifting the line up one unit will result in adding one to the y-intercept.

When the line is shifted left two units, the  variable must be replaced with the  term.

Use the distributive property to expand this equation.

The new equation is:  

The answer is:  

Shifting the line up two units will add two to the y-intercept.

Shifting the line left three units mean that the x-variable will be replaced with: 

Replace  with the quantity of .

Simplify this equation by combining like-terms

The answer is:  

Expand the equation by distribution.

Since this line is shifted left two units, replace the  variable with .

The equation becomes:

The new equation after the shift is:  

The answer is:  

If a line is shifted ten units to the left, the x-variable will be replaced with  since the root will be ten units to the left of the original location.

The equation becomes:

Simplify the linear equation.

The answer is: