Solve the quadratic equation by completing the square.
1 answer:
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Answer:
The equation of a parallel line in the slope-Intercept form that contains the point (3,-2) is:
- y = 2x- 8
Step-by-step explanation:
The slope-intercept form of the line equation
y = mx+b
where
- m is the slope
- b is the y-intercept
Given the equation of a line
y = 2x + 4
comparing with the slope-intercept form of the line equation
The slope of the line AB is m = 2
We know that the parallel lines have the same slope.
Thus, the slope of the new line is also 2.
now we have,
- The slope of new line m = 2
- The point = (3, -2)
Using the point-slope form of the line equation
where m is the slope of the line and (x₁, y₁) is the point
substituting the values m = 2 and the point (x₁, y₁) = (3, -2)
y - (-2) = 2(x - 3)
y + 2 = 2x - 6
subtracting 2 from both sides
y + 2 - 2 = 2x - 6 - 2
y = 2x- 8
Therefore, the equation of a parallel line in the slope-Intercept form that contains the point (3,-2) is:
- y = 2x- 8
Answer:
Option C.
Step-by-step explanation:
From the table attached,
Pre-image coordinates J(-8, 2) → Image coordinates J'(-22, 5.5)
J(-8, 2) → J'(-22, 5.5)
Since, rule for the dilation of a point is,
(x, y) → (kx, ky) [Here k = scale factor of dilation]
Therefore, kx = -22
k(-8) = -22
k =
k = 2.75
So the scale factor should be 2.75
From the given options,
Option A.
(x, y) →
→ 0.36(x, y)
But value of k should be 0.36
Therefore, Incorrect option.
Option B.
(x, y) →
→ 0.14(x, y)
k = 0.14
But the value of k should be 2.75
Incorrect option.
Option C.
(x, y) →
→ 2.75(x, y)
k = 2.75
Therefore, this option is correct.
Option D.
(x, y) →
→ 7.33(x, y)
k = 7.33
But the scale factor should be 7.33
Incorrect option.