how do you graph the following equations 6x+y=2 and x-6y=6 using the slope and y intercept

Question

i need to graph these equations and determine the number of solutions ive tried everything and I am still stuck.. help!

Answer 1

The equations are

     -------->(1)

    --------->(2)

From (1)

The above equation compare with .

Slope m=-6 and y-intercept is 2. From (1)

The above equation compare with .

Slope m=1/6 and y-intercept is -1.

Graph:

From the graph Slope of the 1 st line and

Slope of the 2 nd line .

Answer 2

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

The first equation is 6x + y = 2.

y = - 6x + 2.

Compare the above equation with slope - intercept form y = mx + b.

slope = - 6 and y - intercept is 2.

y - intercept is 2, so the line crosses the y - axis at (0, 2).

Using slope find the next point.

Slope = rise/run = - 6/1

Start at point (0, 2), move 6 units down and 1 unit right, then plot the point (1, - 4).

The second equation is x - 6y = 6.

6y = x - 6

y = (1/6)x - 1.

Compare the equation with slope - intercept form y = mx + b.

slope = 1/6 and y - intercept is - 1.

y - intercept is - 1, so the line crosses the y - axis at (0, - 1).

Using slope find the next point.

Slope = rise/run = 1/6

Start at point (0, - 1), move 1 unit up and 6 units right, then plot the point (0, 6).

Draw the lines through these points.

Graph :

Observe the graph, the solution of the equations is (x, y ) = (0.48, - 0.91).