Question

Graph and then find the solution for y=1/2x+2 and y=-1/4x+8

Answer 1

To graph the equations y = 1/2x + 2 and y = -1/4x + 8, we can create a table of values and plot the points on a coordinate plane.

For y = 1/2x + 2:
x | y
-----
-4 | 0
0 | 2
4 | 4
8 | 6

Plotting these points, we get a line that has a positive slope and passes through the point (0, 2).

For y = -1/4x + 8:
x | y
-----
-8 | 10
0 | 8
8 | 6
16 | 4

Plotting these points, we get a line that has a negative slope and passes through the point (0, 8).

Here is the graph of both equations:

{{{ graph( 300, 200, -10, 20, -5, 15, (1/2)x+2, (-1/4)x+8) }}}

To find the solution to these equations, we can look for the point of intersection on the graph.

From the graph, we can see that the lines intersect at the point (4, 4). Therefore, the solution to the system of equations is x = 4 and y = 4.