# Linear Equations

Determine if the given ordered pair is a solution to the equation:

4. -3x + y = -2 (0,2)

6. 2x - y = -3 (-2, -1)

Find the specified values:

8. 6x - 3y = 12 x-intercept & y-intercept

10. 4x - 2y = 6 slope & y-intercept

Re-write the equations in the specified form:

12. y = 2x -3 write in standard form (Ax + By = C)

Derive the slope - intercept equations:

14. Slope = -3, passing through point (-2,3)

16. Passing through points (3, -4) & (-2, -1)

Â© BrainMass Inc. brainmass.com December 24, 2021, 6:58 pm ad1c9bdddfhttps://brainmass.com/math/linear-algebra/linear-equations-153546

## SOLUTION This solution is **FREE** courtesy of BrainMass!

Please see the attached file for the complete solution.

Thanks for using BrainMass.

Determine if the given ordered pair is a solution to the equation:

4. -3x + y = -2 (0,2)

No, as -3*0 + 2 =2.

6. 2x - y = -3 (-2, -1)

Yes, as 2*(-2) -(-1)=-4+1=-3.

Find the specified values:

8. 6x - 3y = 12 x-intercept & y-intercept

To get y-intercept, we let x=0. From 6x - 3y = 12, we have

6*0 - 3y = 12

So,

-3y=12

So, y=-4. Hence, the y-intercept is (0, -4).

To get x-intercept, we let y=0. From 6x - 3y = 12, we have

6x - 3*0 = 12

So,

6x=12

So, x=2. Hence, the x-intercept is (2, 0).

10. 4x - 2y = 6 slope & y-intercept

To get y-intercept, we let x=0. From 4x - 2y = 6, we have

4*0 - 2y = 6

So,

-2y=6

So, y=-3. Hence, the y-intercept is (0, -3).

To get the slope, we can write 4x - 2y = 6 as

2y =4x- 6

So,

y=2x-3

So, the slope is equal to 2.

Re-write the equations in the specified form:

12. y = 2x -3 write in standard form (Ax + By = C)

If we move 2x from the right hand side to the left hand side, then we get

y - 2x = -3

i.e.,

-2x+y=-3

Derive the slope - intercept equations:

14. Slope = -3, passing through point (-2,3)

Using a formula, we know the equation is

y-3=-3[x-(-2)]

i.e.,

y-3=-3x-6

so,

y= -3x-3

16. Passing through points (3, -4) & (-2, -1)

The slope is

Using a formula, we know the equation is

y-(-4)=(-3/5)[x-3]

i.e.,

y+4=(-3/5)x+9/5

so,

y=(-3/5)x -11/5

i.e.,

Â© BrainMass Inc. brainmass.com December 24, 2021, 6:58 pm ad1c9bdddf>https://brainmass.com/math/linear-algebra/linear-equations-153546