Chapter ISG, Problem 4.2.5P

a.

To determine

To write equation for the given table.

Answer to Problem 4.2.5P

The equation of line is, $y-95=8(x-10)$

Explanation of Solution

Given information:

The total caps and price relation is,

Number of caps	Price
5	55
10	95
15	135
20	175

Formula Used:

Equation of line is,

  $y-y1=m(x-x1)$

Slope is,

  $m=\frac{y2-y1}{x2-x1}$

Calculation:

For slope, substituting the value,

  $m=\frac{95-55}{10-5}$

So,

  $m=\frac{40}{5}$

On solving,

  $m=8$

For the equation of line, substituting the value,

  $y-95=8(x-10)$

Conclusion:

The equation of line is, $y-95=8(x-10)$

b.

To determine

To calculate the number of caps if the budget is $200

Answer to Problem 4.2.5P

23 caps can be ordered.

Explanation of Solution

Given information:

The equation of number of caps and price relation is, $y-95=8(x-10)$

Total money Sonia has is $200

Concept Used:Equation solving

Calculation:

Substituting the values in the equation,

  $200-95=8(x-10)$

So,

  $102=8(x-10)$

Cross-multiplying both sides,

  $\frac{102}{8}=x-10$

On solving,

  $12.75=x-10$

Shifting right hand side values to left hand side,

  $x=12.75+10$

On solving,

  $x=22.75$

Rounding off the value,

  $\approx 23$

Hence, she can order 23 caps.

Conclusion:She can order 23 caps.

c.

To determine

To graph the equation.

Explanation of Solution

Given information:

The equation of number of caps and price relation is, $y-95=8(x-10)$

Graph: