Write an equation of the line perpendicular to the given line that contains p. p(4, -3); y=1/2x+3. write an equation for the line in point-slope form.

y = 2x - 5

Step-by-step explanation:

First, we must find the slope of the current equation.

This is the number in front of the x.

Seeing as this is 1/2x, the slope of this line is 1/2

When finding the slope of a line perpendicular, you need to find the

So, in this case it is:

This gives the result -2, so the gradient on the perpendicular line is -2

Now, to find the equation of a line, you need to use:

y - y1 = m(x - x1)

Where y1 and x1 are the values in the coordinates (4 , -3)

So y1  = -3, x1 = 4, and m is a half. Plug these values in:

y - 3 =2(x - 4)

Expand the brackets by multiplying the contents by two:

x * 2 = 2x

-4 * 2 = -8

2x - 8

y - 3 = 2x -8

And now simply move the -3 over to the other side, making it a positive:

y = 2x - 8 + 3

Simplify:

y = 2x - 5

So the equation of the line is y = 2x - 5

-3

step-by-step explanation:

a drawing really does here:

so i draw the horizontal line y=2 and the vertical line x=-2 at this intersection i put b (this is where my right angle is going to be).   so point b is at (-2,2).   point a is 5 units long and is also on y=2 so this point has to be (3,2) or (-7,2) -doesn't matter i will go with (3,2).

now we know c is at (-2,y) we don't know the y yet bet we know that c is on x=-2.

we have the area of the triangle is .5bh=12.5

we know the base length is 5 (ab)

we have the height is (2-y) if you look at your

plug in

.5(5)(2-y)=12.5

solve for y to get the y-coordinate for c

2.5(2-y)=12.5

divide both sides by 2.5 giving:

2-y=5

now subtract 2 on both sides

-y=3

y=-3

answer: a video game has three difficulty levels: easy, medium, and expert. the game's scoring works in such a way that a player has to score a fixed number of points to advance to the next level, and then the scoring starts over. the total score needed to clear all three difficulty levels is 7,500. two times the number of points needed to clear the easy level is 500 more than the number of points needed to clear the medium level. twice the number of points needed to clear the medium difficulty level is 1,500 more than the number of points needed to clear the expert level. if x, y, and z represent the easy, medium, and expert levels, respectively, and a is the coefficient matrix of the system of equations modeling this situation, identify the inverse matrix, a-1, and the solution matrix, x, of the system of equations.

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