Match each equation to the ordered pair that represents one of its solutions. 3x+2y=6, -5x+y=-10, x-4y=8, -6x-5y=30 ordered pairs - (0,-6) (0,3) (4,-1) (1,-5)

For this problem, I would put all the equations in slope-intercept form (y = mx + b) and graph each one.

1) 3x + 2y = 6

Subtract 3x from both sides of the equation.

2y = -3x + 6

Divide all terms by 2.

y = -3/2x + 3

The graph of this line has a y-intercept of 3 and a negative slope of 3/2. Note that the line has a y-intercept of three which means it crosses the coordinate (0,3).

Solution: (0,3)

2) -5x + y = -10

Add -5x to both sides of the equation.

y = 5x - 10

The graph of this line has a y-intercept of -10 and a slope of 5. If the line's y-intercept is -10 and the slope is positive 5, then the line will have to rise 5 units and run 1 unit to the left.

(0, -10) → (1, -5)

Solution: (1, -5)

3) x - 4y = 8

Subtract x from both sides of the equation.

-4y = -x + 8

Divide all terms by -4.

y = x/4 - 2

y = 1/4x - 2

The line has a y-intercept of -2 and a slope of 1/4. If the line's y-intercept is -2 and the slope is 1/4, then the line will have to rise 1 unit and run 4 units to the left.

(0, -2) → (4, -1)

Solution: (4, -1)

4) By process of elimination, we'll know that the equation of -6x - 5y = 30 should have the solution of (0, -6). However, it's good to check the answer.

-6x - 5y = 30

Add -6x to both sides of the equation.

-5y = 6x + 30

Divide all terms by -5.

y = -6/5x - 6

The y-intercept is (0, -6) and the slope is 6 units down over 5 units to the right.

Solution: (0, -6)