Answer in standard form Write the equation of the line parallel to 4x + 3y = 9 and passing through the point (-6,2)

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sciencesolve | Teacher | (Level 3) Educator Emeritus

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You need to evaluate first the equation using the point slope form, then you need to convert it into the standard form.

The point slope form of the equation of line is the following, such that:

`y - y_0 = m(x - x_0)`

`(x_0,y_0)` represent the coordinates of the point that lies on the line whose equation you need to determine

m represents the slope of the line

The problem provides the coordinates `x_0 = -6` and `y_0 = 2` and the information that the line you need to determine is parallel to the line `4x + 3y = 9` , hence, you need to use the following equation that relates the slopes of two parallel lines, such that:

`m_1 = m_2`

You need to convert the equation of the line `4x + 3y = 9` into the slope intercept form, `y = mx + n` , to evaluate the slope, such that:

`3y = -4x + 9 => y = (-4/3)x + 9/3 => m_2 = -4/3 => m_2 = -4/3`

Hence, you have all the information required to write the equation of the line, such that:

`y - 2 = (-4/3)(x + 6) => y - 2 + (4/3)x + 8 = 0 => 4x + 3y + 18 = 0`

Hence, evaluating the standard form of equation of line, under the given conditions, yields `4x + 3y + 18 = 0.`

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