Question

# In the x - y plane, the graph of line has slope 3 . Line k is parallel to line and contains the point ( 3, 10 ). Which of the following is an equation of line k ?

Hint:

**Hint:**

We know that the slopes of parallel lines are equal in a xy-plane. So, we get slope of k and a point on line k . We use the point slope form of a line to find the equation of k . The point slope form of a line is y - a = m( x - b ) , where m is slope and (a, b) is a point on the line.

## The correct answer is:

### Given,

Slope of line = 3

As, line is parallel to , their slopes are equal.

So, slope of line k (m) = 3

Also, passes through the point (3, 10)

The equation of a line in point-slope form is given by

where, m is the slope of the line and

( a, b ) is any point lying on the line.

Using the above formula, the equation of line is given by

Simplifying the above equation, we have

Adding 10 both sides, we get

Finally, we have

Hence, the equation of line k is y = 3x + 1

Thus, the correct option is D)

**Note:**

The general equation of a line is Ax + By = c. This form is modified to give us many other forms of equation of a line which involve the use of slope, x intercept, y intercept, etc. The student needs to be familiar with all these forms of equation of a line.

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We could also calculate the standard deviation for both the data sets

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Where,

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**Note:**

We could also calculate the standard deviation for both the data sets

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Where,

= standard deviation

= total number of terms

= terms given in the data

= mean

After finding both the standard deviations, we can compare them. This is a tedious task and needs precision.