Find equation of a line that is parallel to y= (-5/6)x - 6 and passes through the point (5, -5)

Question

Also the equation of a perpendicular line to that same equation and passes through the points (-5, 5)

Answer 1

If you are familiar with point-slope form as shown in the other answer, that is a great way to answer questions like these! However, in case you're not as familiar with that form, here's a way to use a familiar slope-intercept form (y = mx + b) to answer this question.

Remember that in the equation y = mx + b, m represents the slope of the line and b represents the y-intercept of the line.

To find the equations of lines that are parallel and perpendicular to a given line, the first step is to identify the slope of your given line. The given line is y = (-5/6)x - 6. The slope of the line is the coefficient of x (the number in front of x), so the slope of the given line is -5/6.

(The y-intercept of the given line won't matter when figuring out the rest of the question.)

QUESTION 1: PARALLEL LINE

Remember that the parallel lines have the SAME SLOPE. That means that the slope of the line that is parallel to our given line is also -5/6, so we can substitute that into the equation directly, and now we have y = (-5/6) x + b.

The line is supposed to pass through (5, -5), so we will substitute this coordinate in the (x, y) of the equation:

-5 = (-5/6) (5) + b

-5 = -25/6 + b

-5/6 = b

So the equation of the PARALLEL line is y = (-5/6) x - 5/6

QUESTION 2: PERPENDICULAR LINE

Remember that the slope of perpendicular lines are NEGATIVE RECIPROCALS of each other. That means that the slope of the line that is perpendicular to our given line is 6/5, so we can substitute that into the equation directly, and now we have y = (6/5) x + b.

The line is supposed to pass through (-5, 5), so we will substitute this coordinate in the (x, y) of the equation:

5 = (6/5) (-5) + b

5 = -6 + b

11 = b

So the equation of the PERPENDICULAR line is y = (6/5) x + 11

Answer 2

I always like to check after equation is formed. plug in x value, does y = value for y

y = -5x/6 - 5/6

x=5, y=-30/6=-5,,,checked

As for perpendicular line, the slope now must be -(1/(-5/6))=6/5

all lines with slope 6/5 are perpendicular to any line with slope -5/6

have 6/5=(y-(-5))/(x-5)

careful with algebra and check final answer by plugging in x=5 and make sure y=--5

Answer 3

y+5 =(-5/6)(x-5) in point slope form

or

y = -5x/6 + 25/6 -30/6

y = -5x/6 - 5/6 in slope intercept form

or

5x +6y = -5 in standard form