Point-slope form of a line: We need a point (x₀,y₀) and the slope "m";
y-y₀=m(x-x₀)
We have the next equation of line:
y=1/2 x-2 (slope-intercept form y=mx+b)
the slope of this line is 1/2 (m=1/2)
And any one point could be:
if x=0; then y=1/2 (0)-2=-2 (0,-2)
Therefore, we already have the point (0-,2) and the slope (m=1/2)
y-y₀=m(x-x₀)
y+2=1/2(x-0)
Answer: the point slope form of y=1/2 x-2; would be:
y+2=1/2(x-0)
B + (-2) = 0
Here, we need to do the inverse operation, and apply it to BOTH sides of teh equation.
b -2 = 0
+2 +2
b = 2
Now we have our answer, b = 2
Final answer: b = 2
Let n = number of glasses needed
1 glass gives us 1*0.4 = 0.4 liters of water
2 glasses give us 2*0.4 = 0.8 liters
3 glasses give us 3*0.4 = 1.2 liters
4 glasses give us 4*0.4 = 1.6 liters
and so on...
In general,
n glasses give us n*0.4 = 0.4*n liters of water
So 0.4*n is going to be the same as 3.4 as we want to fill the 3.4 liter pitcher.
Set 0.4*n equal to 3.4 and solve for n
0.4*n = 3.4
0.4*n/0.4 = 3.4/0.4 <<--- divide both sides by 0.4
n = 8.5
If we want n to be a whole number, then round up to the nearest whole number. So we'll need 9 full glasses of water to fill the 3.4 liter pitcher. There is extra water in this case which isn't used.
So the answer is either 8.5 or 9 depending on if your teacher wants you to round to the nearest whole number.
