how would i graph y=x+3 -4x+4y=28
what steps?
To graph the equations y=x+3 and -4x+4y=28, you can follow these steps:
1. Solve both equations for y to obtain the slope-intercept form (y=mx+b), where m represents the slope and b is the y-intercept.
- For the equation y=x+3, the slope is 1 and the y-intercept is 3.
- For the equation -4x+4y=28, rearrange it to obtain y= (4x+28)/4 = x + 7. The slope is 1, and the y-intercept is 7.
2. Plot the y-intercepts for both equations on the graph. For y=x+3, plot the point (0,3), and for y=x+7, plot the point (0,7).
3. Use the slope to find additional points on the graph. The slope of 1 means that for every one unit increase in the x-coordinate, the y-coordinate will increase by 1. Use this information to find at least one more point on each line. For instance, for y=x+3, if you move one unit to the right from the point (0,3), you get (1,4). For y=x+7, if you move one unit to the right, you get (1,8).
4. Plot these additional points on the graph.
5. Connect the points for each equation using a straight line. The line for y=x+3 should pass through the points (0,3) and (1,4). The line for -4x+4y=28 should pass through the points (0,7) and (1,8).
6. Check if the lines intersect or are parallel. If the lines intersect at a point, this is the solution to the system of equations. If they are parallel, there is no solution.
Here is a visualization:
(graph to be inserted)