Hi Michele;

-4x+9y=9

This equation is NOT in standard form...

Ax+By=C, A is greater than zero.

-4 is not greater than zero.

Let's multiply both sides by -1 to correct this...

(-1)(-4x+9y)=(9)(-1)

4x-9y=-9

The second equation is in standard form...

x-3y=-6

Slope is -A/B

4x-9y=-9, slope is -(4/-9)=4/9...as the line moves up 4 units, it moves 9 units to the right.

x-3y=-6, slope is -(1/-3)=1/3...as the line moves up 1 units, it moves 3 units to the right.

Both equations have y-intercepts, the value of y when x=0...

4x-9y=-9...[(4)(0)]-9y=-9...-9y=-9...y=1...(0,1)

x-3y=-6....(0)-3y=-6...-3y=-6...y=2...(0,2)

Both equations have x-intercepts, the value of x when y=0...

4x-9y=-9...4x-[(-9)(0)]=-9...4x=-9...x=-9/4...(-9/4,0)

x-3y=-6....x-[(3)(0)]=-6...x=-6...(-6,0)

The two lines must cross. Let's calculate the values of this coordinate...

4x-9y=-9

x-3y=-6

Let's take the second equation...

x-3y=-6

and multiply both sides by 4...

4(x-3y)=4(-6)

4x-12y=-24

With the coefficient of x being the same, 4, let's subtract one equation from the other to establish the value of y...

4x-9y=-9

-(4x-12y=-24)

3y=15

y=5

Let's plug this into either equation to establish the value of x. I randomly choose the first...

4x-9y=-9

4x-[(9)(5)]=-9

4x-45=-9

4x=36

x=9

Coordinate is (9,5)...

Let's plug both values into the second equation to verify results...

x-3y=-6

9-[(3)(5)]=-6

9-15=-9

-9=-9

With the slopes of both equations, 4/9 and 1/3, the coordinates of their y-intercepts, (0,1) and (0,2) and their x-intercepts, (-9/4,0) and (-6,0), as well as the point at which the two lines cross, (9,5), you can graph.