Question

Plot the following linear equations and then plot the solution.

(The last point you plot should be the solution)

y=-x+6

y=3x-2

Answer 1

(2, 4)

Explanation:

Both equations have been solved for y, so to find x we need only set the equations = to each other: y=-x+6 = y=3x-2

Combining like terms, we get 4x = 8, and x = 2. Substituting 2 for x in y = 3x -2, we get y = 3(2) - 2 = 4.

The solution is (2, 4). If you were to graph these two lines, you'd find that they intersect at (2, 4).

Answer 2

See below

Explanation:

(1) Create a table containing a few values of x and y

I chose x = -5, 0, and 5.

`\begin{array}{rcc}& \mathbf{y = x + 6} & \mathbf{y = 3x - 2}\\\mathbf{x} & \mathbf{y} & \mathbf{y}\\-5 & 1 & -17\\0 & 6 & -2\\5 & 11 & 13\\\end{array}`

(2) Plot your points

Draw dots at the coordinates of each point ( Fig. 1).

(3) Draw the graph

Draw smooth lines through the points for each function.

Extend the lines in both directions to the edges of the plot area.

Your graphs should look like Fig. 2.

(4) Plot the solution

Note where the lines cross.

They appear to intersect at (4, 10).

Plot the point, and the finished graph should look like Fig. 3.