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.

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 equation of a line, , the slope is represented by the variable .

In this case the line has a slope of .

Therefore the answer is .

The point resides in quadrant I (the upper right quadrant), so both values must both be positive. The only possible solution 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 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 ). 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 ). 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 .

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

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

In this case

First flip the sign to get .

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 slope-intercept form of a line, , the slope is represented by the variable .

In this case the line

has a slope of .

The answer is .