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Rina8888 [55]
3 years ago
5

What is the equation of the line that passes through the point (4, 6) and is parallel to the line 2y - 4x = 1?

Mathematics
1 answer:
Cloud [144]3 years ago
7 0

Answer:

D. y = 2x - 2

Step-by-step explanation:

1) First, find the slope of the given line. Place it in slope-intercept form to identify its slope easily. Isolate the y in the equation:

2y-4x = 1\\2y = 4x+1\\y = 2x+\frac{1}{2}

A line placed in slope-intercept form is represented by the formula y = mx + b. The m, or the coefficient of the x-term, represents the slope. Thus, the slope of this line is 2.

2) Lines that are parallel share the same slope. So, the slope of the parallel line will have 2 as its slope as well.

We now have enough information to write the equation of the line in point-slope form. From there, we can convert it to slope-intercept form and find out which option is correct.

Use the point-slope formula y-y_1 = m (x-x_1) and substitute values for m, x_1, and y_1. Since m represents the slope of the line, substitute 2 in its place. Since x_1 and y_1 represent the x and y values of a point the line intersects, substitute the x and y values of (4,6) into the formula as well. Then, with the resulting equation, isolate y like before to find which option is correct:

y-6 = 2(x-4)\\y-6 = 2x-8\\y = 2x-2

So, option D is correct.  

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The complete proof for the given parallelogram is given in the image attached below.

<h3>What is a Parallelogram?</h3>

A parallelogram is a quadrilateral whose opposite sides are parallel and also congruent to each other.

The complete proof would be as shown below:

1. ABCD is a parallelogram [given]

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3. ∠1 ≅ ∠2, ∠3 ≅ ∠4 [alternate interior angles theorem]

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Identify an equation in point slope form for the line parallel to y=1/2x-7 that passes through (-3,-2)
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Answer:

Step-by-step explanation:

The point slope form of a straight line is expressed as

y - y1 = m(x - x1)

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