Consider the line y=6x-1 Find the equation of the line that is perpendicular to this line and passes through the point (2,-2). Find the equation of the line that is parallel to this line and pass...

Question

Consider the line y=6x-1

Find the equation of the line that is perpendicular to this line and passes through the point (2,-2).

Find the equation of the line that is parallel to this line and passes through the point (2,-2).

Answer 1

The first step is to find the slope of the new line. The slope of the existing line is 6, so we take the negative reciprocal to find that the new slope will be -1/6. With that, we can start filling in y=mx+b with our slope m. So now we have y = -1/6x + b and can determine b by plugging in the point we were given. That gives -2 = (-1/6 * 2) + b. Now we can solve for b as -5/3, which gives a final equation of y = -1/6x - 5/3.

For the parallel line, we keep the original slope of 6 and plug in our point (2,-2) to find b. From -2 = (6*2) + b, we know that b is -14. So the final equation for the parallel line is y = 6x - 14.

Answer 2

y=6x -1 has a perpendicular line with equation y=-x/6 + b

to find b, plug in the point x=2, y=-2

-2 = -(2)/6 +b

b = -2+1/3 = -5/3

perpendicular line is y=-x/6 -5/3

a parellel line is y=6x +b

plug in x=2, y=-2

-2 =6(2) +b

b = -2-12=-14

the parallel equation is y=6x -14

parallel lines have the same slope = the coefficient of the x term, when the linear equation is solved for y

perpendicular lines have negative inverse slope. take 6 = 6/1, flip it upside down and change its sign, =-1/6

Answer 3

A line perpendicular to another means they have negative reciprocal slopes. In other words, if one has a slope or 4/3 then the other will have a slope of -3/4. If one has a slope of -2, then the other will have a slope of 1/2.

What is the slope of y = 6x - 1. It is in slope-intercept form (y = mx + b) so the number in front of the "x" is the slope (m). That number is 6.

Now you know the slope of the line you are looking for, it is the negative reciprocal of 6, or -1/6. You also know a point on that line (2, -2). You can use the point slope form of a line to find the equation of the line. The point slope form is: y - y₁ = m(x - x₁). You just have to plug in x₁ = 2, y₁ = -2, and m = -1/6

To find the line parallel to it, use the same process except that a parallel line has a slope EQUAL to the given line. So, use the point-slope form of the line again, but use x₁ = 2, y₁ = -2, and m = 6