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)
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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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