You want to get familiar with what the slope-intercept form equation means. even though the discussion board covers some of this... slope-intercept is y = mx + b, and in it, x and y are a point on your graph (x, y), m is the slope, and b is your y-intercept. in word problems, any constant will typically be b.
but, really, to answer this word problem, you don't have to think so hard about y = mx + b. just read the problem and bring your information together:
"the venue will cost $1500 to rent for an evening"
"$25 per person"
so they only gave you two bits of information, and you just have to decide where they fit. if the venue costs $1500 for an evening, that's a fixed cost--the 1500 isn't going to go up or down depending on the number of people at the charity event. it stays. you're paying 1500 regardless, even if 2 people show up. because the discussion board states that b should represent your starting amount, you're automatically $1500 in the hole, because you have to spend that much to get the venue. you will, however, write it as a positive integer, because the question wants you to calculate the total cost, by my understanding--you're adding the cost of the people with the cost of the venue.
$25 is not a fixed amount. if it's $25 per person, then if 2 people come, it costs $50, if 3 people arrive, it costs $75. this cost is dependent upon the number of people, which you can call "x"
with that information, write any other equation you would for a word problem:
y = 25x + 1500
that's your equation, and it just so happens that this equation is in y = mx + b format. the x-value represents the number of people who show up for the charity; the y-value represents the overall cost.
and you need three solutions for this equation--which, luckily, is a quick and easy process!! choose an x-value and solve for y.
y = 25x + 1500
when x = 1...
y = 25(1) + 1500
y = 25 + 1500
y = 1525
ordered pair: (1, 1525)
when x = 2...
y = 25(2) + 1500
y = 50 + 1500
y = 1550
ordered pair: (2, 1550)
when x = 3...
y = 25(3) + 1500
y = 75 + 1500
y = 1575
ordered pair: (3, 1575)
i hope that helped!!
Answer:
n = -7
Step-by-step explanation:
Solve for n:
-3 n - 5 = 16
Hint: | Isolate terms with n to the left-hand side.
Add 5 to both sides:
(5 - 5) - 3 n = 5 + 16
Hint: | Look for the difference of two identical terms.
5 - 5 = 0:
-3 n = 16 + 5
Hint: | Evaluate 16 + 5.
16 + 5 = 21:
-3 n = 21
Hint: | Divide both sides by a constant to simplify the equation.
Divide both sides of -3 n = 21 by -3:
(-3 n)/(-3) = 21/(-3)
Hint: | Any nonzero number divided by itself is one.
(-3)/(-3) = 1:
n = 21/(-3)
Hint: | Reduce 21/(-3) to lowest terms. Start by finding the GCD of 21 and -3.
The gcd of 21 and -3 is 3, so 21/(-3) = (3×7)/(3 (-1)) = 3/3×7/(-1) = 7/(-1):
n = 7/(-1)
Hint: | Simplify the sign of 7/(-1).
Multiply numerator and denominator of 7/(-1) by -1:
Answer: n = -7
