AskSia

Plus

Find the equation of the line that is parallel to the line 2y+6x=4 and passes th...

Jul 23, 2024

Find the equation of the line that is parallel to the line 2y+6x=4 and passes through the point (-1,5).

Solution by Steps

step 1

To find the slope of the line given by the equation

2y + 6x = 4

, we first rewrite it in slope-intercept form

y = mx + b

step 2

Starting with

2y + 6x = 4

, we solve for

y

2y = -6x + 4

y = -3x + 2

step 3

The slope

m

of the line is

-3

step 4

To find the equation of a line parallel to

y = -3x + 2

that passes through the point

(-1, 5)

, we use the point-slope form of the equation of a line:

y - y_1 = m(x - x_1)

step 5

Substituting

m = -3

and the point

(-1, 5)

into the point-slope form:

y - 5 = -3(x + 1)

step 6

Simplifying the equation:

y - 5 = -3x - 3

y = -3x + 2

Answer

The equation of the line that is parallel to

2y + 6x = 4

and passes through the point

(-1, 5)

y = -3x + 2

Key Concept

Parallel lines have the same slope.

Explanation

To find the equation of a line parallel to a given line, we use the same slope and apply the point-slope form with the given point.