Equation of the line.Find the equation of the line parallel to the graph of 4x+2y=8 and containing (-1;5).

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justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

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The slope of two parallel lines is the same. The slope of 4x+2y=8 can be determined by writing it in the slope-intercept form

4x + 2y = 8

=> 2y = -4x + 8

=> y = -2x + 4

The slope is -2

The line parallel to this has the slope -2 and as the point (-1, 5) lies on it, the equation of the line is:

y - 5 = -2*(x + 1)

=> y - 5 = -2x - 2

=> 2x + y - 3 = 0

The equation of the required line is 2x + y - 3 = 0

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giorgiana1976 | College Teacher | (Level 3) Valedictorian

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For 2 lines to be parallel, their slopes have to be equal. For this reason, we'll put the given equation of the line in the point slope form.

y = mx + n

For this reason, we'll subtract 4x both sides:

2y=8 - 4x

We'll divide by 2:

y = -2x + 4

Comparing, we'll get the slope of the first line: m1 = -2

The slope of the parallel line is m2 = -2.

The line is passing through the point  (-1;5). The equation of the parallel line is:

y - 5 = -2(x + 1)

We'll add 5:

y = -2(x + 1) + 5

We'll remove the brackets:

y = -2x - 2 + 5

We'll combine like terms:

y = -2x + 3

The equation of the parallel line is:

y = -2x + 3

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