Determine the equation of a line that passes through A(2,5) and is parallel to the line defined by 3x−y+12=0. State the equation in slope y-intercept form

y = 3x - 1

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

3x - y + 12 = 0 ( subtract 3x + 12 from both sides )

- y = - 3x - 12 ( multiply through by - 1 )

y = 3x + 12 ← in slope- intercept form

with slope m = 3

Parallel lines have equal slopes , thus

y = 3x + c ← is the partial equation

To find c substitute (2, 5) into the partial equation

5 = 6 + c ⇒ c = 5 - 6 = - 1

y = 3x - 1 ← equation of parallel line

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