Question

State whether the lines are parallel, perpendicular, coinciding, or neither: 6x+3y=–15 and y–3=–2x

Answer 1

Answer:

Parallel

Step-By-Step Explanation:

Put the Function in Slope Intercept Form and Find the Slope of 6x+3y = 15

6x+3y = 15

3y = -6x + 15

3y/3 = -6x/3 + 15/3

y = -2x + 5

We can see that the slope of 6x+3y = 15 is -2

Put the Function in Slope Intercept Form and Find the Slope of y–3=–2x

y–3=–2x

y = -2x + 3

Here are our two Functions In Slope Intercept Form

y = -2x + 5

y = -2x + 3

Remember the m = slope and the b = y-intercept

y = mx + b

y = -2x + 5

y = -2x + 3

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We can see both equations have the same slope of -2 so this means they could be parallel because parallel functions have the same slope but coinciding functions have the same slope too. To tell if the two functions are coinciding, the functions need to have the same slope and the same y-intercept. Looking at the two functions, we can see they have the same slope of -2 but their y-intercept are different so this makes the two functions parallel.