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

Since linepis perpendicular to linem, this means that the products of the slopes ofpandmmust be–1:

(slope ofp) * (^-1/₂) = -1

Slope ofp= 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 linep。The answer is 2x – y = 3.

Perpendicular slopes are opposite reciprocals.

The given slope is found by converting the equation to the slope-intercept form.

The slope of the given line isand the perpendicular slope is。

We can use the given point and the new slope to find the perpendicular equation. Plug in the slope and the given coordinates to solve for the y-intercept.

Using this y-intercept in slope-intercept form, we get out final equation:。

The definition of a perpendicular line is one that has a negative, reciprocal slope to another.

For this particular problem, we must first manipulate our initial equation into a more easily recognizable and useful form: slope-intercept form or。

一个ccording to ourformula, our slope for the original line is。We are looking for an answer that has a perpendicular slope, or an opposite reciprocal. The opposite reciprocal ofis。Flip the original and multiply it by。

我们的答案的斜率。Search the answer choices forin theposition of theequation.

is our answer.

(As an aside, the negative reciprocal of 4 is。把整数除以一个然后翻转/不gate. This does not apply to the above problem, but should be understood to tackle certain permutations of this problem type where the original slope is an integer.)

Putting the first equation in slope-intercept form yields。

一个perpendicular line has a slope that is the negative inverse. In this case,。

To start, begin by dividing everything by, this will get your equation into the format。This gives you:

Now, recall that the slope of a perpendicular line is theoppositeandreciprocalslope to its mutually perpendicular line. Thus, if our slope is,然后垂直的直线的斜率μst be。Thus, we need to look at our answers to determine which equation has a slope of。在给出的选项中,只有一个相匹配es this is。If you solve this for, you will get:

For two lines to be perpendicular their slopes must have a product of。
and so we see the correct answer is given by

Perpendicular lines have slopes whose product is。

Looking at our equations we can see that it is in slope-intercept form where the m value represents the slope of the line,

。

In our case we see that

therefore,。

Since

we see the only possible answer is

。

Since linefollows the equation, we can surmise its slope is。Thus, it follows that any line perpendicular towill have a slope of。

Since we also know at least one point on line,, we can use point slope form to find an initial equation for our line.

---->。

Next, we can simplify to reach point-slope form.

---->。

Thus, linein slope-intercept form is。

In order to solve this problem, we need first to transform the equation from standard form to slope-intercept form:

Transform the original equation to find its slope.

First, subtractfrom both sides of the equation.

Simplify and rearrange.

Next, divide both sides of the equation by 6.

The slope of our first line is equal to。Perpendicular lines have slopes that are opposite reciprocals of each other; therefore, if the slope of one is x, then the slope of the other is equal to the following:

Let's calculate the opposite reciprocal of our slope:

The slope of our line is equal to 2. We now have the following partial equation:

We are missing the y-intercept,。Substitute the x- and y-values in the given pointto solve for the missing y-intercept.

一个dd 4 to both sides of the equation.

Substitute this value into our partial equation to construct the equation of our line:

First, we must solve the equation foryto determine the slope:y= 2x+³/₂

By looking at the coefficient in front ofx, we know that the slope of this line has a value of 2. To fine the slope of any line perpendicular to this one, we take the negative reciprocal of it:

slope =m, perpendicular slope = –¹/_m

slope = 2 , perpendicular slope = –¹/₂