Question

11. Write an equation for a line that is parallel to the line 6x - 3y = 15 and goes through the point
(-2,4).

Answer 1

Answer:

y = 2x + 8

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Given

6x - 3y = 15 ( subtract 6x from both sides )

- 3y = - 6x + 15 ( divide all terms by - 3 )

y = 2x - 5 ← in slope- intercept form

with slope m = 2

Parallel lines have equal slopes, thus

y = 2x + c ← is the partial equation

To find c substitute (- 2, 4) into the partial equation

4 = - 4 + c ⇒ c = 4 + 4 = 8

y = 2x + 8 ← equation of parallel line

Answer 2

The required equation of the parallel line is,

$6x-3y+24=0$

Equation of parallel lines:

Parallel lines are lines that never intersect. Because of this, a pair of parallel lines have to have the same slope, but different intercepts (if they had the same intercepts, they would be identical lines).

Given, the equation of the line is $6x-3y=15$

Let the equation of the parallel line be,

$6x+3y+k=0$...(1)

Since, the equation (1) passes through the point (-2,4) then,

$6(-2)-3(4)+k=0\\-12-12+k=0\\k=24$

Now, substituting $k=24$  in equation (1) we get,

$6x-3y+24=0$

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