How do you graph y equals x plus 1 and y equals negative x plus 7 and what is the solution to the system?

Answer 1

Plotting Points Method

For y = x+1, let the first 7 coordinates be:

x = 0, 1, 2, 3, 4, 5, 6
y = 1, 2, 3, 4, 5, 6, 7

For y = -x+7, let the first 7 coordinates be:

x = 0, 1, 2, 3, 4, 5, 6
y = 7, 6, 5, 4, 3, 2, 1

Plot the graph and where the lines intersect that will be the solution to the simultaneous equation:

x = 3 and y = 4 -- (3,4).

Slope Intercept Method

For y = x + 1, the y-intercept is 1 (the point (0,1)) and the slope is 1.

You can graph y = x + 1 by plotting the point (0,1) and drawing a line with slope of 1 (through the point (1, 2) for example).

For y = -x + 7, the y-intercept is 7 (the point (0,7)) and the slope is -1.

To graph the function, plot the point (0,7) and draw the line with slope -1 through that point (through the point (1,6) would work).

The solution to the system is found by substituting x + 1 for y in the second equation:

y = x + 1
y = -x + 7
x + 1 = -x + 7
2x = 6
x = 3.
y = x + 1
y = 3 + 1 = 4.

So the solution is at the point (3,4).