What is the slope of a line with the equation y=3x+2? What would be the equation of a line perpendicular and a line parallel to the line of the equation above?
This question uses slope-intercept form, which has an equation of y=mx+b. m is the slop value and b is the value of the y-intercept. In this case, we are looking for the slope, which appears in the equation given to be 3. Now that you know the slope of the line, you can figure out equations that would make a line perpendicular to the given line. A perpendicular line has a slope that is the opposite reciprocal of that line. The opposite would mean making the positive number a negative number, or vise versa. A reciprocal is when you switch the numerator and denominator of the slope. So if we have a slope of 3, its opposite reciprocal would be -1/3. A parallel of a line has an identical slope of the given line but a different y-intercept, or b value. You can change the b value to whatever you want and it will be a parallel line as long as you keep the slope the same! ex. y=3x-7
Factor this quadratic: x^2-5x+4
In order to factor a quadratic you have to understand its format: ax^2+bx+c. When you factor, you are finding the values that make this equation equal to zero. Find 2 numbers that multiply to equal the c value (in this case, 4) and add to be the b value (in this case, -5). For this problem, those numbers would be -4 and -1 because -4 x -1 = 4 and -4 + -1 = -5. That means that x^2-5x+4 expand to (x-4)(x-1), and if you multiply that using distribution, you will end up with the original quadratic.
What is the order of notes in the first inversion of a G major chord?
The answer is B G D. The notes in a G major chord are G, D, and B, however, in the first inversion, the major third of the chord is always in the bottom. B is the third in a G major scale, therefore, B would come first in the order of notes in the chord!