An equation of the form y=ax+b, where y and x are variables, and a and b are constants, is called a linear equation.
The reason it is called linear is because the graph of the equation is a line.
The line passes through the origin only if b=0, as in our problem.
Any line (except vertical lines) represents a proportional relationship in that the change in y is proportional with the change in x. It is not a condition that the line passes through the origin.
In our specific case, y=(1/5)x, means that the change in y is always 1/5 of the change in x. That is, if x changes by 5 units, y changes by 1. If x changes by 10 units, y changes by 2, and so on.
So, the constant of proportionality is 1:5, or 0.2.
Answer:
y = 5x - 3
Step-by-step explanation:
As we move from the point (-2, -13) to the point (1, 2), we see the x-value (the 'run') increasing by 3 and the y-value (the 'rise') increasing by 15. Therefore the slope of the line passing thru these two points is m = rise / run = 15/3, or m = 5.
Using the slope-intercept formyula y = mx + b, we find the y-intercept as follows, using 1 for x, 2 for y and 5 for m:
2 = 5(1) + b, or
b = -3
Then the desired equation is
y = 5x - 3
Answer:
see below
Step-by-step explanation:
V = l*w*h for the rectangular tank
V = 70* 40*40
=112000 cm^3 = 1mL
The water is 84000
Make this a fraction
84000/112000 = 3/4
The water fills 3/4 of the tank
1-3/4 = 1/4
It is 1/4 from the top
Find the volume of the treasure chest
V = 12*10*8 =960
Tower
V = pi r^2
3.14 * 10^2 *10
=3140
Water + chest + tower
84000+960+3140 =88100
This is less than 112000 so the water will not overflow
Answer:
a.= 24 b.=-21 c. is x=-7 or 3
Step-by-step explanation:
