Question

For the graph y = 41 find the slope of a line that is perpendicular to it and the slope of a line parallel to it. Explain your answer with two or more sentences.

Answer 1

the slope of a line perpendicular to line y=41: is undefined because the line y=41 is a horizontal line that has 0 slopes, and any line perpendicular to it will be a vertical line, which means it has no slope.

the slope of a line parallel to line y=41: also has 0 slopes because the line y=41 does too.

Answer 2

Answer: Hello mate!

in a linear function y = ax + b, the slope is the number a, and the x-axis intercept is the number b.

Here we have the function y = 41, which is a constant function, and in the graph, you can see that this graph is parallel to the x-axis, you can see that this function has a slope equal to 0.

If you want a perpendicular line, you need a constant in the x-axis, this can be something like x = 10, wich is graphed with a line parallel to the y-axis, and you can see that this is perpendicular to y = 41. Then the slope of this function is infinity and its undefined. (this function does not exist)

For the parallel line, every other y = constant is a parallel to our function y = 41, for example, we can take y = 12.

Now, the slope of this function is 0.

A rule in linear equations is: two linear equations are parallel if they have the same slope and a different x-axis intercept; you can see that every y = constant function has a slope of 0, and then all of them are parallel.

For a perpendicular line, if your function is of the form y = ax + b, a perpendicular line is of the form y' = (-1/a)x + c, where c can be any constant.

Again, because in our problem a is equal to 0, here we have a division by 0, and this is why this line is undefined.