We can solve the system of equations using the substitution method.

Solve for in the second equation.

Substitute this value of into the first equation.

Now we can solve for .

Solve for using the first equation with this new value of .

The solution is the ordered pair .

We can solve the system of equations using the substitution method.

Solve for in the second equation.

Substitute this value of into the first equation.

Now we can solve for .

Solve for using the first equation with this new value of .

The solution is the ordered pair .

Rewrite this equation in slope intercept form .

Add on both sides.

The equation becomes:

Divide by two on both sides.

The equation in slope intercept form is:

Shifting this equation down four units means that the y-intercept will be decreased four units.

The answer is:

Rewrite this equation in slope intercept form .

Add on both sides.

The equation becomes:

Divide by two on both sides.

The equation in slope intercept form is:

Shifting this equation down four units means that the y-intercept will be decreased four units.

The answer is:

A horizontal line has infinitely many values for , but only one possible value for . Thus, it is always of the form , where is a constant. Horizontal lines have a slope of . The only equation of this form is .

A horizontal line has infinitely many values for , but only one possible value for . Thus, it is always of the form , where is a constant. Horizontal lines have a slope of . The only equation of this form is .

The equation for a vertical line is where is the -coordinate of the point on the line.

As such, the equation for the line containing the point is,

.

Think about what it means to be a horizontal line. The value changes to be any real number, but the value always remains constant. Thus, we are looking for an equation in which the value is constant and the value is not present. This would be any equation of the form , where is a constant.

Think about the meaning of a vertical line on the coordinate grid. The value changes to any value, yet the value always stays the same. Thus, we are talking about an equation in which the is free, or is not effected, and the is constant. This is an equation of the form , where is a constant.

In order for a line to be considered horizontal, there must be zero slope.

In the slope-intercept equation, , the value of must be zero.

The answers that have an existing slope are incorrect.

The equation is a step function, and is not a horizontal line.

The only answer that satisfies a horizontal line is:

The answer is: