Choose the equation of the

Question

line passing through the point (1, -5) and parallel to y = 2x + 4

Answer 1

Given y = 2x+4

And given point ( 1,-5 )

( 1,-5 ) = ( x,y ) Therefore x=1 and y = -5

The line parallel to y = 2x +4 is y = 2x  + k---------------(1)

Substitute the given point in (1)

-5 = 2(1) + k

-5 = 2 + k

k = -2-5

k = -7

Substitute k = -7 in (1)

y = 2x - 7

Therefore line passing through the point (1,-5) and parallel to y = 2x +4 is 2x - y - 7 = 0

 

Answer 2

Slope-intercept form line equation is y = mx + b, where m is slope and b is y-intercept.

The line equation is y = 2x + 4.

Comapare the equation with slope - intercept form.

Slope (m) = 2.

Because the parallel lines have same slopes, the slope of parallel line through the point (1, - 5) is 2.

Now the parallel line equation is y = 2x + b.

Find the y - intercept by substituting the point in the parallel line equation say (x, y) = (1, - 5).

- 5  = (2)(1) + b

b = - 5 - 2

⇒ b = - 7.

The parallel line equation is y = 2x - 7.