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 .

We know that the slope of the original line is

Thus the slope of the perpendicular line is the negative reciprocal of , or –2.

Then we plug the slope and point (5, 6) into the form , which yields

When we simplify this, we arrive at

Putting the first equation in slope-intercept form yields .

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

Using the slope intercept formula, we can see the slope of line p is ¼. Since line k is perpendicular to line p it must have a slope that is the negative reciprocal. (-4/1) If we set up the formula y=mx+b, using the given point and a slope of (-4), we can solve for our b or y-intercept. In this case it would be 17.

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The equation of line p is given in the form y = mx + b, where m is the slope and b is the y-intercept. Because the equation is y = –x + 4, the slope is m = –1.

If two lines perpendicular, then the product of their slopes is equal to –1. Thus, if we call n the slope of a line perpendicular to line p, then the following equation is true:

m(n) = –1

Because the slope of line p is –1, we can write (–1)n = –1. If we divide both sides by –1, then n = 1. In short, the slope of a line perpendicular to line p must equal 1. We are looking for the equation of a line whose slope equals 1.

Let's examine the answer choices. The equation y = –x – 4 is in the form y = mx + b (which is called point-slope form), so its slope is –1, not 1. Thus, we can eliminate this choice.

Next, let's look at the line x + y = 4. This line is in the form Ax + By = C, where A, B, and C are constants. When a line is in this form, its slope is equal to –A/B. Therefore, the slope of this line is equal to –1/1 = –1, which isn't 1. So we can eliminate x + y = 4. Simiarly, we can eliminate the line x + y = –4.

The line y = –4 is a horizontal line, so its slope is 0, which isn't 1.

The answer is the line y = x + 4, because it is the only line with a slope of 1.

The answer is y = x + 4.

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.

We are asked to find the equation of the line that is the perpendicular bisector of AB. If we find a point that the line passes through as well as its slope, we can determine its equation. In order for the line to bisect AB, it must pass through the midpoint of AB. Thus, one point on the line is the midpoint of the AB. We can use the midpoint formula to determine the midpoint of AB with endpoints (5, –2) and (–3, 10).

The x-coordinate of the midpoint is located at (5 + –3)/2 = 1.

The y-coordinate of the midpoint is located at (–2 + 10)/2 = 4.

Thus, the midpoint of AB is (1, 4).

So, we know that the line passes through (1,4). Now, we can use the fact that the line is perpendicular to AB to find its slope. The product of the slopes of two line segments that are perpendicular is equal to –1. In other words, if we multiply the slope of the line by the slope of AB, we will get –1.

We can use the slope formula to find the slope of AB.

slope of AB = (10 – (–2))/(–3 – 5) = 12/–8 = –3/2.

Since the slope of the line multiplied by –3/2 must equal –1, we can write the following:

(slope of the line)(–3/2) = –1

If we multiply both sides by –2/3, we will find the slope of the line.

The slope of the line = (–1)(–2/3) = 2/3.

Thus, the line passes through the ponit (1, 4) and has a slope of 2/3.

We will now use point-slope form to determine the line's equation. Let's let m represent the slope and (x1, y1) represent a ponit on the line.

y – y = m(x – x1)

y – 4 = (2/3)(x – 1)

Multiply both sides by 3 to get rid of the fraction.

3(y – 4) = 2(x – 1)

Distribute both sides.

3y – 12 = 2x – 2

Subtract 3y from both sides.

–12= 2x – 3y – 2

Add 2 to both sides.

–10 = 2x – 3y.

The equation of the line is 2x – 3y = –10.

The answer is 2x – 3y = –10.

First, we want to identify the slope of our given line. In slope-intercept form, a line's slope is the coefficient of .

The slope of our given line is .

Now, we can start to find the perpendicular line. Remember that in order for two lines to be perpendicular, their slopes must be negative reciprocals of each other.

In this case, we want to find a line whose slope is the negative reciprocal of . So, we want a line whose slope is .

With this in mind, the only answer choice with a slope of is .

Therefore, the perpendicular line is .

The given equation is in standard form, so it must be converted to slope-intercept form: y = mx + b to discover the slope is –2/3. To be perpendicular the new slope must be 3/2 (opposite reciprocal of the old slope). Using the new slope and the given point we can substitute these values back into the slope-intercept form to find the new intercept, –5. In slope-intercept form the new equation is y = 3/2x – 5. The correct answer is this equation converted to standard form.

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 .