To solve this, first put the linear equation into slope-intercept form:

.

Recall that in slope intercept form

,

the m term is the slope value.

Therefore, the slope is 2.

The graph of a quadratic function  has an -intercept at any point  at which , so, first, set the quadratic expression equal to 0:

The number of -intercepts of the graph is equal to the number of real zeroes of the above equation, which can be determined by evaluating the discriminant of the equation . Set , and evaluate:

The discriminant is positive, so there are two real solutions to the quadratic equation, and the graph of the function has two -intercepts.

Let's start by looking at the given equation:

The inequality is written in slope-intercept form; therefore, the slope is equal to  and the y-intercept is equal to .

All of the graphs depict a line with slope of  and y-intercept . Next, we need to decide if we should shade above or below the line. To do this, we can determine if the statement is true using the origin . If the origin satisfies the inequality, we will know to shade below the line. Substitute the values into the given equation and solve.

Because this statement is true, the origin must be included in the shaded region, so we shade below the line.

Finally, a statement that is "less than" or "greater than" requires a dashed line in the graph. On the other hand, those that are "greater than or equal to" or "less than or equal to" require a solid line. We will select the graph with shading below a dashed line.

Do the first row first and use x and y to represent your variable.

Solve for x by isolating the variable.

We are only given the points the line intersects. This can be used to find the slope of the line, knowing that slope is rise/run, or change in /change in  or by the formula,

.

By substituting, we get

 for the slope.

To find the  intercept, we can use the equation , where  ---> .

Since both given points are on the line, either can be used to solve for :

 --> 

 --> 

Lines that are perpendicular have negative reciprocal slopes. Therefore, the line perpendicular to  must have a slope of . Knowing that the slope of  is , only  has a slope of .

This question is very simple once you realize that a line that will never intersect another line must have the same slope (parallel lines will never intersect). Therefore you must look for the choice that has a slope of . Each answer can be converted to the form  or by knowing that in the equation , the slope of the line is simply . In the correct answer, , the slope would be , which simplfies to .

*Note* the y-intercept is irrelevant to finding the correct answer.

If the equation shifts left three units, the  term will become .  

The equation shifting up one unit will change the y-intercept of the equation.

Rewrite the equation and distribute to simplify.

The correct equation is: 

Straight-line equations may be written in the slope-intercept form: .

In this form,  equals the slope of the line and  corresponds to the y-intercept.

The given line has a slope of  and a y-intercept of positive . A line that is parallel to another has the same slope. Therefore, the slope of the new line will have to be .

In order to shift a line down, you must change the y-intercept. Since we are moving the line down by  the y-intercept should be  because .

If we plug those values into the slope-intercept equation, then we have the answer: .