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.
