Linear Equations

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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.,

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