What is the equations of a line that is parallel to y = -3x + 6 and contains the point (-3,-5)?

2 Answers
Alan P.
Jun 21, 2018

y=−3x−14

Explanation:

Any line parallel to y=−3x+6
will be in the form y=−3x+c for some constant c

If (x,y)=(−3,−5) is a solution to such an equation, then replacing y with (−5) and x with (−3) gives
−5=(−3)⋅(−3)+c

→−5=9+c

→c=−14

So the desired parallel line would have the equation
y=−3x−14

David G.
Jun 21, 2018

The equation of the line parallel to y=−3x+6 that passes through the point (−3,−5) is:

y=−3x−14

Explanation:

The line y=−3x+6 is already in 'slope-intercept' form, so we can just read off the slope (gradient) as being −3.

We want a line with a gradient of −3 (because that's what 'parallel' means - having the same gradient) that passes through the point (−3,−5).

Take the form y=mx+c and substitute in the 3 things we already know: the slope, one value of x and one value of y:

−5=(−3)(−3)+c

c is the y-intercept of the line: the y coordinate of the point at which it cuts the y axis (which is the line x=0).

−5=9+c

Subtract 9 from both sides:

−14=c

That means the equation of the line is y=−3x−14

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