Lines - SAT Math

First, we must solve the equation for y to determine the slope: y = 2_x_ + 3/2

By looking at the coefficient in front of x, 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

Find the slope of the given line. The perpendicular slope will be the opposite reciprocal of the original slope. Use the slope-intercept form (y = mx + b) and substitute in the given point and the new slope to find the intercept, b. Convert back to standard form of an equation: ax + by = c.

First we find the slope of line M by using the slope formula (_y_2 – _y_1)/(_x_2 – _x_1).

(–5 – 2)/(3 – 2) = –7/1. This means the slope of Line M is –7. A line perpendicular to Line M will have a negative reciprocal slope. Thus, the answer is y = (1/7)x + 3.

First rearrange the equation so that it is in slope-intercept form, resulting in y=2/3 x + 14/9. The slope of this line is 2/3, so the slope of the line perpendicular will have the opposite reciprocal as a slope, which is -3/2.

Perpendicular lines have slopes that are the opposite of the reciprocal of each other. In this case, the slope of the first line is -2. The reciprocal of -2 is -1/2, so the opposite of the reciprocal is therefore 1/2.

The question puts the line in point-slope form y – y1 = m(x – x1), where m is the slope. Therefore, the slope of the original line is 1/2. A line perpendicular to another has a slope that is the negative reciprocal of the slope of the other line. The negative reciprocal of the original line is _–_2, and is thus the slope of its perpendicular line.

The slope of line m is the (y2 - y1) / (x2 - x1) = (5-7) / (-2 - 3)

= -2 / -5

= 2/5

To find the slope of a line perpendicular to a given line, we must take the negative reciprocal of the slope of the given line.

Thus the slope of line k is the negative reciprocal of 2/5 (slope of line m), which is -5/2.

The equation of a line is where is the slope.

Rearrange the equation to match this:

For the perpendicular line, the slope is the negative reciprocal;

therefore

First we must find the slope of the given line. The slope of y = –3x – 4 is –3. The slope of the perpendicular line is the negative reciprocal. This means you change the sign of the slope to its opposite: in this case to 3. Then find the reciprocal by switching the denominator and numerator to get 1/3; therefore the slope of the perpendicular line is 1/3.

First, solve for the equation of the line in the form of y = mx + b so that you can determine the slope, m of the line:

8x + 16y = 48

16y = -8x + 48

y = -(8/16)x + 48/16

y = -(1/2)x + 3

Therefore the slope (or m) = -1/2

The slope of a perpendicular line is the negative inverse of the slope.

m = - (-2/1) = 2

We know that the line passes through point B, but we must calculate its slope in order to find the equation that defines the line. Because the line is tangent to the circle, it must make a right angle with the radius of the circle at point B. Therefore, the slope of the line is perpendicular to the slope of the radius that connects the center of the circle to point B. First, we can find the slope of the radius, and then we can determine the perpendicular slope.

The radius passes through points C and B. We can use the formula for the slope (represented as ) between two points to find the slope of the radius.

Point C: (2,-5) and point B: (7,-3)

This is the slope of the radius, but we need to find the slope of the line that is perpendicular to the radius. This value will be equal to the negative reciprocal.

Now we know the slope of the tangent line. We can use the point-slope formula to find the equation of the line. The formula is shown below.

Plug in the give point that lies on the tangent line (point B) and simplify the equation.

Multiply both sides by two in order to remove the fraction.

Distribute both sides.

Add to both sides.

Subtract six from both sides.

The answer is .

Looking at the graph, we can tell the slope of the line is 3 with a -intercept of , so the equation of the line is:

A perpendicular line to this would have a slope of , and would pass through the point so it follows:

A slope perpendicular to another line can be found by taking the reciprocal of the orignal slope and changing the sign.

If you solve for in the given equation,

divide by three on each side

.

There is a slope of because the equation is in slope-intercept form where m represents the slope,

.

The reciprocal of that with a changed sign is

.

The line is a vertical line. The line perpendicular to a vertical line must always have a slope of zero.

The only valid answer with a slope of zero is:

Let's write the equation of the given line in slope-intercept form.

The slope of the given line is expressed by the coefficient of x. The slope here is .

To find the slope of the perpendicular line, we take the negative reciprocal of the given line's slope. Therefore, the slope of the perpendicular line is .

To solve, simply use the midpoint formula as outlined below.

Given,

Thus,

A line segment has endpoints (0,4) and (5,6). To find the midpoint, use the midpoint formula:

X: (x1+x2)/2 = (0+5)/2 = 2.5

Y: (y1+y2)/2 = (4+6)/2 = 5

The coordinates of the midpoint are (2.5,5).

You can find the midpoint of each coordinate by averaging them. In other words, add the two x coordinates together and divide by 2 and add the two y coordinates together and divide by 2.

x-midpoint = (-3 + 5)/2 = 2/2 = 1

y-midpoint = (7 + -9)/2 = -2/2 = -1

(1,-1)

The correct answer is (6, 6). The midpoint formula is ((x1 + x2)/2),((y1 + y2)/2) So 1 + 11 = 12, and 12/2 = 6 for both the x and y coordinates.

midpoint = ((x1 + x2)/2, (y1 + y2)/2)

= ((–1 + 3)/2, (2 – 6)/2)

= (2/2, –4/2)

= (1,–2)