Question

The equation of straight line passing through the point (1,2) and parallel to the line y = 3x + 1 is
(a) y + 2 = x + 1
(b) y + 2 - 3 * x + 1)
(c)y - 2 - 3* (x-1)
(d) y - 2 = x-1​

Answer 1

Answer:

Option c : y - 2 = 3 (x - 1)

Step-by-step explanation:

Given:

• The line passes through the point (1, 2)
• It is parallel to the line y = 3x + 1

To Find:

• The equation of the straight line

Solution:

Given that the straight line is parallel to the line y = 3x + 1 which is in the form y = mx + c where m is the slope of the line.

Hence slope of the parallel line = 3

Given that the lines are parallel, ie slope of the two lines are equal.

Hence slope of the straight line = 3

Also by given, the straight line passes through the point (1, 2)

By one point form, if we know the slope and a point on the line the equation of a line is given by,

$\tt m=\dfrac{y-y_0}{x-x_0}$

Substitute the data,

$\tt 3=\dfrac{y-2}{x-1}$

Cross multiplying,

3 (x - 1) = y - 2

Therefore the equation of the line is y - 2 = 3 (x - 1).

Hence option c is correct.

Answer 2

Answer:

• Correct option is (c).

Step-by-step explanation:

Given:

• The straight line passing through the point (1, 2).
• Same line parallel to the line y = 3x + 1.

To Find:

• The equation of that straight line.

Formula used:

• (y - y₁) = m(x - x₁), where m = slope of line.

Now, we know that,

∴ General equation of line, i.e. y = mx + c

⇒ y = 3x + 1

Hence, slope of line (m) = 3.

Now, It is given that the straight line is passing through the point (1, 2).

⇒ (y - y₁) = m(x - x₁)

Substitute the values,

⇒ (y - 2) = 3(x - 1)

∴ Equation of straight line = (y - 2) = 3(x - 1)

Hence, Correct option is (c).