What is the slope of a line that is perpendicular to a line whose equation is −2y=3x+7 ? enter your answer in the box.

The slope of the line that is perpendicular to a line whose equation is -2y = 3x + 7 is 2/3.

For lines to be perpendicular to each other, the product of there slopes is equals to negative 1. This can be mathematically represented as follows

m₁ × m₂ = -1

where

m₁ and m₂ are slopes of the lines.

Therefore,

let's find the slope of the equation given

-2y = 3x + 7

divide both sides by -2

y = -3/2 x + 7/2

Using the slope equation model,

y = mx + c

where

m = slope

The slope in our equation will be - 3/2.

Using the first formula for perpendicular lines,

m₁ × m₂ = -1

-3/2 m₁= -1

m₁  = -2/-3

m₁ = 2/3

The slope of the line is 2/3

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for the friend request.

when a figure, such as triangle (xyz) is reflected over the line y = x to create x'y'z' the x-coordinates and y-coordinates of the original image (pre-image) will be reversed for the image. (e.g., (x, y) > (y, x)) this means that the pre-image position of the x- and y-coordinates switch places which in turn provides a mirror like image of the original xyz.  

i notice that when i draw a line segment from x to x', that the points are parallel from each other -- they are exactly across from each other and do not intersect with any other points.  

yes, think i would see the same characteristic if you drew the line segment connecting y with the reflecting line and then y' with the reflecting line because of the essence of reflections. because it is a mirror image, each point was effected the same way which leads me to conclude that they same would apply to y and y'.