Question

Write an equation of the line passing through the point (-7,-6) that is parallel to the line y=3x+2

Answer 1

Answer:  y = 3x+15

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Explanation:

Parallel lines have equal slopes but different y intercepts.

The slope of y = 3x+2 is m = 3 (compare it to y = mx+b)

Any parallel line will also have slope m = 3

The parallel line goes through (x1,y1) = (-7, -6)

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Turn to point-slope form. Plug in the values mentioned and solve for y

y-y1 = m(x-x1)

y-(-6) = 3(x-(-7))

y+6 = 3(x+7)

y+6 = 3x+21

y = 3x+21-6

y = 3x+15

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Or you could use slope intercept form

y = mx+b

y = 3x+b

-6 = 3(-7)+b

-6 = -21+b

-6+21 = b

15 = b

b = 15

Since m = 3 and b = 15, we know the equation is y = 3x+15