Question

Please help, I don't really understand.

Answer 1

The equation is y = -6x + 6
The slope of a parallel line is -6. That’s because the slope of 2 lines must be the same for it to be parallel. If a line has a slope of 77, the line parallel to it will also have a slope of 77.

The slope for a perpendicular line is 1/6. That’s because you need to find the opposite reciprocal. In order to do that, change -6 into a fraction form, which is -6/1. Then, flip the numerator and denominator so it’s -1/6. Lastly, multiply it by negative 1 to get 1/6.
The 2 slopes of the original and perpendicular line multiply together to get -1.

Hope this helps!

Answer 2

Explanation:

The standard form of a linear equation is y=mx+b, where m is the slope and b is the y-intercept. Let's rewirite the given equation to match this format:

y = 6 - 6x

y = -6x + 6

The slope is -6 and the y-intercept is 6. The slope tells us the angle the line is taking. A negative slope such as this means that the line is angled down as it goes from left to right. The size of the number tells us just how steep the line is.

All parallel lines have the same slope. Any line with the format of y = -6 + b will be parallel. See the attached graph for proof. The graph shows several parallel lines to y=-6+b, including the three top lines, all with the same slope, but with three different values for b: +6, 0, and +10.

Perpendicular lines have a slope that is the negative inverse of the reference line, in this case y = -6x + 6. A perpendicular line will have a slope of -(1/-6) or 1/6 [the negative inverse of -6]. Perpendicular lines will have the form y = (1/6)x + b. See the attached graph. The three bottom equations are all perpendicular to y=-6x+6. All have the same slope (1/6), but differnt y-intercepts (b = 0, 6, and 10). The y-intercept numbers for both the parallel and perpendicular lines were randomly chosen, simply to illustrate the possibilities.

In summary,

"Slope of a parallel line" is -6, and

"Slope of perpendicular line" is (1/6)