The equation of ramp 1 is y = 2x + 7 and the equation of ramp 2 is y = 3 x + 7. Which is the safest ramp ?

Answer 1

Ramp 1 gradient is 2
Ramp 2 gradient is 3
A car , with brake off, is more likely to run away on Ramp 2.

Ramp 1 is safer.

Answer 2

R1 is defined for y as

y = 2x + 7,

while R2 is

y = 3x + 7.

Simply graphing the equation should give you an answer, but, since we don't have a graphing calculator at hand, we'll do it the old-fashioned way.

for x = 1

R1 >> y = 2(1) + 7 = 2 + 7 = 9

R2 >> y = 3(1) + 7 = 3 + 7 = 10

for x = 2

R1 >> y = 2(2) + 7 = 4 + 7 = 11

R2 >> y = 3(2) + 7 = 6 + 7 = 13

With that, we can find the slope of each ramp. The lowest slope, by logic, is the one found in the safest ramp.

Slope = (y_2 - y_1) / (x_2 - x_1)

R1 >> (11 - 9) / (2 -1) = 2 / 1 = 2

R2 >> (13 - 10) / (2 - 1) = 3 / 1 = 3

Therefore, Ramp 1 is the safest.

(However, if you want a much easier method, you can use the one explained by the fellow just above me.)

Answer 3

In an equation of the form y = ax + b, a is the gradient of the line (or ramp in this case) and b is the value where the line crosses the y axis (ie x = 0). A lower gradient is less steep and, presumably, a less steep ramp will be safer, therefore you want ramp 1.

Answer 4

Safest?
I'm guessing that you mean the one with the lowest slope.

If thats the case, then the answer is Ramp 1
For it has the lowest slope out of the two.

You can tell by the integer next to the variable. The greater the number (over zero), the steeper the slope.

You will be able to see this more clearly when you start graphing the equations.

Hope this helps!
Good luck! It gets much harder ^_^

Answer 5

Assuming you're escaping from a natural disaster and speed is of the essence, you'll want to take ramp 2. It will get you away from the danger faster, and is therefore the safer ramp.

Answer 6

The first ramp is significantly less steep than the 2nd ramp.