write an equation that is parallel to: y=6x-71

perpendicular to y=5x-69

y= -1/6x-71

and
y=-1/5x-69
(i think)

Popcorns first example is wrong

parallel lines have equal slopes, so the 6x has to stay the same
another line parallel would be y = 6x + 1

To find an equation that is parallel to a given line, we need to remember that parallel lines have the same slope. Given the equation y = 6x - 71, we can determine that the slope is 6.

So, any equation that has a slope of 6 will be parallel to y = 6x - 71.

An equation with a slope of 6 can be written as y = 6x + b, where b is the y-intercept.

To find b in this case, we can use the fact that the line passes through the point (0, -71), which is the y-intercept of the given line. We can substitute these values into our equation:

-71 = 6(0) + b
-71 = 0 + b
b = -71

Therefore, an equation parallel to y = 6x - 71 can be written as y = 6x - 71.

Now let's find an equation perpendicular to y = 5x - 69.

To determine a line perpendicular to another line, we need to remember that the slopes of perpendicular lines are negative reciprocals of each other. The negative reciprocal of 5 is -1/5.

So, any equation with a slope of -1/5 will be perpendicular to y = 5x - 69.

An equation with a slope of -1/5 can be written as y = (-1/5)x + b.

To find b, we can use the fact that the line passes through the point (0, -69), which is the y-intercept of the given line. We can substitute these values into our equation:

-69 = (-1/5)(0) + b
-69 = 0 + b
b = -69

Therefore, an equation perpendicular to y = 5x - 69 can be written as y = (-1/5)x - 69.

In summary:
- An equation parallel to y = 6x - 71 is y = 6x - 71.
- An equation perpendicular to y = 5x - 69 is y = (-1/5)x - 69.