What is the equation of the line that passes through the point (2,−1) and has a slope of 3/2

Given :-

A line having a slope of 3/2 passes through (2,-1) .

To Find :-

The equation of the line .

Answer :-

According to the question ,

m = 3/2

Point = (2,-1)

We know Point slope form of the line as ,

y - y¡ = m ( x - x ¡ )

Substitute ,

y - (-1) = 3/2 ( x - 2 )

y + 1 = 3/2x - 3/2*2

y +1 = 3/2x - 3

2( y +1) = 3/2x *2 - 3*2

2y + 2 = 3x - 6

3x -2y -8 = 0

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'.