Make a table of solutions and graph the equation. x + y = 6

Answer 1

The equation is x + y = 6.

Write the equation in slope-intercept form y = mx + b, where m is slope and b is y - intercept.

y = - x + 6.

Make the table of values to find the solutions that satisfy the equation.

Choose values for x and find the corresponding values for y.

x	y = - x + 6	(x, y )
- 2	y = - (- 2) + 6 = 2 + 6 = 8	(- 2, 8)
-1	y = - (- 1) + 6 = 1 + 6 = 7	(- 1, 7)
0	y = - (0) + 6 = 0 + 6 = 6	(0, 6)
1	y = - (1) + 6 = - 1 + 6 = 5	(1, 5)
2	y = - (2) + 6 = - 2 + 6 = 4	(2, 4)

From the table the solutions are y = 8, 7, 6, 5, and 4, when x = - 2, - 1, 0, 1, and 2.

The points are (- 2, 8), (- 1, 7), (0, 6), (1, 5), and (2, 4).

The equation is y = - x + 6.

Graph :

• Draw the coordinate plane.
• Plot the above points.
• Connect the ploted points.

Then, the formed line indcating given equation.

Answer 2

Sketching the Graph of an Equation by Point Plotting :

1. If possible, rewrite the equation so that one of the variables is isolated on one side of the equation.

The equation is x + y = 6 → y = - x + 6.

2. Make a table of values showing several solution points.

Choose the different values of x, and substitute these values in the original equation to obtain random y - values.

x	y = - x + 6	(x, y)
- 1	y = - (- 1) + 6 = 7	(- 1, 7)
0	y = - (0) + 6 = 6	(0, 6)
1	y = - (1) + 6 = 5	(1, 5)
2	y = - (2) + 6 = 4	(2, 4)
3	y = - (3) + 6 = 3	(3, 3)
4	y = - (4) + 6 = 2	(4, 2)
5	y = - (5) + 6 = 1	(5, 1)

3. Plot these points on a rectangular coordinate system.

4. Connect the points with a smooth line.