Identify the slope and y intercept of the line with equation 2y=5x+4.

For line 2y = 5x + 4 , slope m = and y intercept of line 2y = 5x + 4 is 2.

Step-by-step explanation:

Given:

equation 2y=5x+4.

To find:

The slope and y intercept of the line=?

Solution:

Step 1: Finding the slope intercept form of 2y = 5x + 4

Generic slope intercept form of a line is given by

y = mx + c ,

where m = slope of the line.

2y = 5x + 4

=>

=>

=>

On comparing above slope intercept form of given equation with generic slope intercept form y = mx + c , we can say that for line 2y = 5x + 4 , slope

Step 2: Finding the y intercept:  

y intercept is that point where line is on y – axis and as value of x = 0 at y axis , we can say that y intercept is that value of y when x = 0 .

On substituting x = 0 in given equation of line we get  

=> 2y = 4

=>

=> y=2

Hence y intercept of line 2y = 5x + 4 is 2.

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'.