Considering that slope (m) is defined as rise over run, you can look that the fractional slopes and determine which are steeper or more flat. For example,  is equivalent to up one and over 8 while  is equivalent to up one and over 10. As you can see the slope of the second line "runs" horizontally more than does the first slope and is therefore flatter. Based on this fact one can conclude that the larger the the slope, the steeper the line. So select the largest slope and this is the steepest line. In our case it is  because  is steeper (larger) than  (flatter and a smaller number).

Rewrite the equation in slope-intercept format, .

Subtract two on both sides.

If the equation shifts eight units down, this means that the y-intercept, , would also subtracted eight units.

The correct answer is:  

The only differences among the answer choices is the translation. The translation of a function is determined by , which represents a horizontal translation h units to the right and k units up. In this case, h = 3 and k = 0, which indicates a translation 3 units to the right.

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: