Question

Please help with these math questions

Answer 1

1. Slope intercept form is y=mx+b, where m is slope and b is y-intercept. 
It gave you point (8,12) and slope of -2. 
So you already know the value of m, so so far it's y = -2x + b. 
Plug the coordinates as x and y: 8 for x and 12 for y.
12 = -2(8) + b
12 = -16 + b
28 = b

Adding b in, you get y = -2x + 28

2. Find the slope, then use point-slope form.
Slope is change in y over change in x, or (y2-y1)/(x2-x1). 
m = (9-1)/(2-3) = 8/(-1) = -8

Point slope form: y - y1 = m(x - x1)
y - y1 = -8(x - x1)
Now plug in either of the coordinates as x1 and y1, let's do (3,1). 
y - 1 = -8(x - 3)
y - 1 = -8x + 24
y = -8x + 25

3. Do it the same way as number 2. Choose two points, for example (1,1) and (2,-2). You find m = -3 and get final answer as y=-3x + 4.

4. B = 150 + 80d 
B is account balance, d is number of monthly deposits.
If you rearrange the terms: B = 80d + 150, you see that that is in slope-intercept form y = mx+b, and if you remember from #1 m is the slope. In this case, the variables are changed, so d is the slope here. And the question told you that d, the slope, is the number of monthly deposits. Its coefficient is 80, so Bianca deposits $80/month.

5. 
14a + 16b = 560
16b = 560 - 14a
b = (560 - 14a)/16
b = 560/16 - 14a/16
b = 35 - (7/8)a
b = -(7/8)a + 35