it's asking to write an equation in slope-intercept form for the line with slope -4 and y-intercept 7. then graph the line. please help ​

Equation = y = -4x+7

See the graph below

Step-by-step explanation:

The equation of the line in slope intercept form is expressed as;

y = mx+c

Given

slope m = -4

y-intercept c = 7

Substitute

y = -4x + 7

Get the x intercept.

at y = 0

0 = -4x + 7

4x = 7

x = 7/4

x = 1.75

The x coordinate  (1.75, 0)

Get the y intercept

at x = 0;

y = -4(0)+7

y = 0+7

y = 7

The y coordinate is (0, 7)

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'.

more detail

step-by-step explanation: