Parallel lines have the same slope.

If an equation is in slope-intercept form, , we take the  from our equation and set it equal to the slope of our parallel line.

In this case .

The slope of our parallel line is .

To find the slope of a line with two points you must properly plug the points into the slope equation for two points which looks like

We must then properly assign the points to the equation as  and .

In this case we will make  our  and  our .

Plugging the points into the equation yields 

Perform the math to arrive at 

The answer is .

To find the slope of a line with two points you must properly plug the points into the slope equation for two points which looks like

We must then properly assign the points to the equation as  and .

In this case we will make  our , and  our .

Plugging the points into the equation yields 

Perform the math to arrive at 

The answer is .

The slope of a perpendicular lines has the negative reciprocal of the slope of the original line.

If an equation is in slope-intercept form, , we use the  from our equation as our original slope.

In this case 

First flip the sign 

To find the reciprocal you take the integer and make it a fraction by placing a  over it. If it is already a fraction just flip the numerator and denominator.

Do this to make the slope 

The slope of the perpendicular line is

.

In the standard form of a line, , the slope is represented by the variable  (and the y-intercept is represented by the variable ). In this case, the line  has a slope of .

In the standard form of a line, , the slope is represented by the variable  and the y-intercept is represented by the variable . In this case, the line  has a y-intercept of .

We can verify this answer by substituting  into the equation, since the y-intercept is where the line intersects the y-axis (where ).

.

In the standard form of a line, , the slope is represented by the variable  (and the y-intercept is represented by the variable ). Since parallel lines have the same slope, we would expect the line in question to have the same slope as , or .

In the standard form of a line, , the slope is represented by the variable  (and the y-intercept is represented by the variable ). Since perpendicular lines have opposite slopes, we would expect the line in question to have a slope that is the negative reciprocal of the slope of the line . Since the slope of the line  is , we would expect the perpendicular line to have a slope of .

To determine which set of points is correct, substitute each of the values into the equation and determine if the equation is true.

Correct points:

Incorrect points:

The point resides in quadrant 1, indicating that both the x-value and y-value are positive. The point is given by , where is the number of horizontal units and is the number of vertical units. The image depicts a point that is  units to the right and  units up; therefore  is the correct answer.

Remember that movement to the right or up is positive, while movement to the left or down is negative.