Find the equation of the line parallel to passing through the point .

Question

Find the equation of the line parallel to  passing through the point  .

Quizplus · Accepted Answer

Since the question asks for a line parallel to a given line, we know that the slopes of the two lines are equal. Therefore, we need to find the slope of the given line first.

However, the given equation is not in slope-intercept form (y = mx + b), so we need to rearrange it first:

11ec19db_84b0_9552_9dbe_7d2b6fcc6df6_TBX8673_11 can be rewritten as:

y = (1/2)x + 3

We can see that the slope of this line is 1/2.

Now we need to find the equation of the line that passes through the given point (11ec19db_84b0_9553_9dbe_5502b6f9f074_TBX8673_11). Let's call this point (a,b).

We know that the slope of the new line must also be 1/2, so we can use the point-slope formula:

y - b = 1/2(x - a)

Substituting the coordinates of the given point, we get:

y - 11ec19db_84b0_9553_9dbe_5502b6f9f074_TBX8673_11 = 1/2(x - 11ec19db_84b0_9553_9dbe_5502b6f9f074_TBX8673_11)

Simplifying:

y - 11ec19db_84b0_9553_9dbe_5502b6f9f074_TBX8673_11 = 1/2x - 11ec19db_84b0_9553_9dbe_0b0d50497072_TBX8673_11

y = 1/2x - 11ec19db_84b0_9553_9dbe_0b0d50497072_TBX8673_11 + 11ec19db_84b0_9553_9dbe_5502b6f9f074_TBX8673_11

Simplifying again, we get:

y = 1/2x + 11ec19db_84b0_9553_9dbe_14f7fb7197b8_TBX8673_11

Therefore, the answer is B: 11ec19db_84b0_9555_9dbe_87b14864747e_TBX8673_11.

Find the Equation of the Line Parallel to Passing