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AnnyKZ [126]
3 years ago
8

The cost y to rent an off road vehicle is proportional to the time that you rent it. It costs $48 to rent it for 3 hours. Write

and equation that represents the situation.
Mathematics
1 answer:
Flura [38]3 years ago
8 0

y = 16h is the equation that represents the situation, where "y" is the total cost to rent and "h" is the number of hours

<h3><u>Solution:</u></h3>

Given that, cost y to rent an off road vehicle is proportional to the time that you rent it

Let "y" be the cost to rent the road vehicle

Let "h" be the number of hours rented for

Then, by given statement,

\text{ cost to rent the vehicle } \propto \text{ number of hours rented for }

y \propto h\\\\y = kh -------- eqn 1

Where "k" is the constant of proportionality

<em><u>Given that it costs $ 48 to rent it for 3 hours</u></em>

Therefore, y = 48 and h = 3

48 = k \times 3\\\\k = \frac{48}{3} = 16

<em><u>Substitute k = 16 in eqn 1</u></em>

y = 16 \times h\\\\y = 16h

Thus y = 16h is the equation that represents the situation

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The equation of the line  in ax+by=c  form where a,b,c  are integers with no factor common to all​ three, and greater than or equal 0 is:

x+3y=12

Step-by-step explanation:

Given:

x-intercept = 12

y-intercept = 4

To find the equation of line in the form ax+by=c where a,b,c  are integers with no factor common to all​ three, and greater than or equal 0.

Solution:

The x-intercept is the point at which the line cuts the x-axis. The point of x-intercept is given as (x,0)

Thus, on point of the line is (12,0)

The y-intercept is the point at which the line cuts the y-axis. The point of y-intercept is given as (0,y).

Thus, on point of the line is (0,4)

Using the two points we can find the slope of the line using the slope formula.

m=\frac{y_2-y_1}{x_2-x_1}

So, slope of the line can b given as:

m=\frac{4-0}{0-12}

m=\frac{4}{-12}

m=-\frac{1}{3}

The slope intercept form of the equation of he line is given as:

y=mx+b

where m represents slope of the line and b represents the y-intercept.

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y=-\frac{1}{3}x+4

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3y=3.-\frac{1}{3}x+4(3)

3y=-x+12

Adding x both sides.

3y+x=-x+x+12

3y+x=12

Thus, the equation of the line  in ax+by=c  form where a,b,c  are integers with no factor common to all​ three, and greater than or equal 0 is:

x+3y=12

8 0
3 years ago
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