The horizontal line will always have zero slope.  

In the form , the  term must be zero for a horizontal line.

The forms  and  are non-linear.

A constant is a fixed number that will not change.

The equation  represents a vertical line.

The only possible answer is:  

The horizontal lines have slopes of zero.  This means that the  in the slope-intercept form  would leave only the y-intercept as the part of the equation.

The value of  is any constant.

The equations that start with  are considered vertical lines.

The correct answer is:  

The slope intercept form of an equation  refers to a linear line with a certain slope and y-intercept.

In order for the line to be horizontal, the slope  must equal to zero.

Any equation in the answer choices that has an x-variable is incorrect because this either means that the equation has a existing slope, a vertical line, or it's non-linear.

The best answer is:  

A vertical line has an undefined slope.  This also means that the x-value is fixed for every y-value of the graph.

The slope intercept form for a linear equation is .  If , the slope would indicate that the line is horizontal. 

Any answer that has a  in the equation is incorrect.

The only valid answer is:  

The horizontal line will have a slope of  in the form of .

Recall that perpendicular lines have a slope that is the negative reciprocal of the original slope.

This indicates that the vertical line will have undefined slope.   Vertical lines have a fixed x-value that will not change.  

The answer that is perpendicular to a horizontal line cannot have a y-variable in the equation.

The equation  represents a pair of intersecting lines.

The only possible answer is:  

Slope is defined as rise over run. So a slope of .7 (7/10) is the same as 7 units up and 10 units over. Compare this with the slope of 7 (7/1) which is 7 units up and only 1 unit over. The vertical distance is much greater than the horizontal and thus it is steeper. 

To find an equation of a line, we will always need to know the slope of that line -- and to find the slope, we need at least two points. It looks like we have (0, -3) and (12,0), which we'll call point 1 and point 2, respectively.

Now we need to plug in a point on the line into an equation for a line. We can use either slope-intercept form or point-slope form, but since the answer choices are in point-slope form, let's use that.

Unfortunately, that's not one of the answer choices. That's because we didn't pick the same point to substitute into our equation as the answer choices did. But we can see if any of the answer choices are equivalent to what we found. Our equation is equal to:

which is the slope-intercept form of the line. We have to put all the other answer choices into slope-intercept to see if they match. The only one that works is this one:

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 .

First, we need to find the slope of the line.

In order to move from the lower left point to the upper right point, it is necessary to move up five units and right three units. This is a rise of 5 and a run of 3. makes the slope of the line shown .

We can use this to find the -intercept  using the slope formula as follows:

The lower left point has coordinates . Therefore, we can set up and solve for  in this slope formula, setting :

We calculate the slopes of the lines using the slope formula.

The slope of line  is 

The slope of line  is 

The lines have the same slope, making them either parallel or identical.

Since the slope of each line is 0, both lines are horizontal, and the equation of each takes the form , where  is the -coordinate of each point on the line. Therefore, line  and line  have equations  and .This makes them parallel lines.