We need to find the slope of the given equation by converting it to the slope intercept form:  . 

The slope is  and the perpendicular slope would be the opposite reciprocal, or . 

The new equation is of the form  and we can use the point  to calculate . The next step is to convert  into the standard form of .

Perpendicular slopes are opposite reciprocals.  The original slope is  so the new perdendicular slope is 3.

We plug the point  and the slope  into the point-slope form of the equation:

to get  or in standard form .

First one needs to use one of the two equations to substitute one of the unknowns.

From the second equation we can derive that y = x – 3.

Then we substitute what we got into the first equation which gives us: x + x – 3 = 15.

Next we solve for x, so 2x = 18 and x = 9.

x – y = 3, so y = 6.

These two lines will intersect at the point (9,6).

We are given an equation of a line and told that line A is perpendicular to it.  The slope of the given line is 2.  Therefore, the slope of line A must be , since perpendicular lines have slopes that are negative reciprocals of each other.

The equation for line A will therefore take the form , where b is the y-intercept.

Since we are told that it crosses , we can plug in the point and solve for c:

Then the equation becomes .

To find the x-intercept, plug in 0 for y and solve for x:

The slope of the given line is , and the slope of the perpendicular line is its negative reciprocal, .  We take the new slope and the given point  and plug them into the slope-intercept form of a line, .

Thus, the perpendicular line has the equation , or in standard form, .

We start by add x to the other side of the equation to get the y by itself, giving us 8y =17 + x. We then divide both sides by 8, giving us y= 17/8 + 1/8x. Since we are looking for the equation of a perpendicular line, we know the slope (the coefficient in front of x) will be the opposite reciprocal of the slope of our line, giving us y= -8x + 5 as the answer.

Convert the equation to slope intercept form to get y = –1/3x + 2.  The old slope is –1/3 and the new slope is 3.  Perpendicular slopes must be opposite reciprocals of each other:  m_{1 *} m₂ = –1

With the new slope, use the slope intercept form and the point to calculate the intercept: y = mx + b or 5 = 3(1) + b, so b = 2

So y = 3x + 2

Convert the given equation to slope-intercept form.

The slope of this line is . The slope of the line perpendicular to this one will have a slope equal to the negative reciprocal.

The perpendicular slope is .

Plug the new slope and the given point into the slope-intercept form to find the y-intercept.

So the equation of the perpendicular line is .

First, put the equation of the line given into slope-intercept form by solving for y. You get y = -2x +5, so the slope is –2. Perpendicular lines have opposite-reciprocal slopes, so the slope of the line we want to find is 1/2. Plugging in the point given into the equation y = 1/2x + b and solving for b, we get b = 6. Thus, the equation of the line is y = ½x + 6. Rearranged, it is –x/2 + y = 6.

The slope of m is equal to   ^y2-y1/_x2-x1  =  ^2-4/_5-1 = ^-1/₂                                  

Since line p is perpendicular to line m, this means that the products of the slopes of p and m must be –1:

(slope of p) * (^-1/₂) = -1

Slope of p = 2

So we must choose the equation that has a slope of 2. If we rewrite the equations in point-slope form (y = mx + b), we see that the equation 2x – y = 3 could be written as y = 2x – 3. This means that the slope of the line 2x – y =3 would be 2, so it could be the equation of line p. The answer is 2x – y = 3.