Question

Vhat is the equation of the line that is parallel to the
given line and passes through the point (2, 3)?
O x + 2y = 4
O x + 2y = 8
O 2x + y = 4
O 2x + y = 8

Answer 1

Step-by-step explanation:

second one because

only x+2y=8 passes through the point (2,3)

the proof is 2+2*3=2+6=8

if we replace the given point to the other equations we will take wrong results for example

first equation

x+2y=4. 2+2*3=2+6=8 that is not equal to 4

Answer 2

Slopes of lines which are parallel to each other is same. The equation of the line which is parallel to y = mx + c and passes through (2,3) point is y = m(x-2) + 3

How are parallel straight lines related?

Parallel lines have same slope, since slope is like measure of steepness and since parallel lines are of same steepness, thus, are of same slope.

In the line of the form $y = mx + c$, the coefficient of x, which is 'm' here, is the slope of the line $y = mx + c$

Suppose that the given line be:

$y = mx + c$

(we assume this, because the question is a bit incomplete as the initial line isn't given)

And we've to find the equation of a line which is parallel to the line given above, and passes through (2,3).

Suppose it be:

$y = mx + b$ (as the slope of parallel lines would be same).

This line passes through (2,3), so the equation must be true for (x,y) = (2,3).

Putting it, we get:

$y = mx + b\\3 = m(2) + b\\3 - 2m = b$

Thus, the equation of this line is:

$y = mx + b \\y = mx + (3-2m)\\y = m(x-2) + 3$

Learn more about parallel lines here:

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