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Question

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

$y = - \frac{1}{3} x + 11$
$y = \frac{1}{3} x + 9$
$y = 3 x + 7$
$y = 3 x + 1$

hint 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: $y equals 3 x plus 1$

Given,
Slope of line $l$ = 3
As, line is parallel to $l$ , 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
$y minus b equals m left parenthesis x minus a right parenthesis$
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
$y minus 10 equals 3 left parenthesis x minus 3 right parenthesis$
Simplifying the above equation, we have
$y minus 10 equals 3 x minus 9$
Adding 10 both sides, we get
$y equals 3 x minus 9 plus 10$
Finally, we have
$y equals 3 x plus 1$
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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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: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:

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

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: $y equals 3 x plus 1$