1). what is an equation of the line that is perpendicular to y=−4/5x+3 and passes through the point (4, 12) ? 2). what is an equation of the line that is perpendicular to −x+3y=9 and passes through the point (−3, 2) ?

For 1.) if we need an equation of a line that is perpendicular to the one given, we will need the opposite reciprocal of the slope.  The given slope is -4/5 so the opposite reciprocal is 5/4.  If the line passes through (4, 12), we will use x=4 and y=12 to write a new equation that can be solved for b, the y-intercept.  Here we go.  and 12 = 5 + b.  b = 7.  So the equation you need is .  For 2.) we need to find the slope of the line since it's not apparent the way it is written.  Solve it for y to find the slope.  3y=x+9 and .  The slope is 1/3 so the opposite reciprocal is -3.  That's the perpendicular slope.  Using point (-3, 2) where x = -3 and y = 2, we will write the equation and solve for b. and 2 = 9+b so b = -7.  Our new equation then is y=-3x-7.  There you go!

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step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote , , , so that we can call

1 the 1st term, 3 the 2nd term, 6 the 3rd term,etc.

note the following:

from the 1st term (1) to the 2nd term (3), we go up by 2,from the 2nd term (3) to the 3rd term (6), we go up by 3from the 3rd term (6) to the 4th term (10), we go up by 4, andfrom the 4th term (10) to the 5th term (15), we go up by 5.

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from , to get to , we add

from , to get to , we add

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

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