Chapter ISG, Problem 4.1.1P

a.

To determine

To form an equation for the given situation

Answer to Problem 4.1.1P

The equation is $y=\frac{4}{5}x-8$

Explanation of Solution

Given information: The slope (m) is,

  $slope=\frac{4}{5}$

y- intercept (c) is,

  $y-\mathrm{int}ercept=-8$

Formula Used: The equation of line in terms of slope and intercept

  $y=mx+c$

Calculation:

Substituting the values,

  $y=\frac{4}{5}x+(-8)$

On solving,

  $y=\frac{4}{5}x-8$

Conclusion:The equation is $y=\frac{4}{5}x-8$

b.

To determine

To form an equation for the given situation

Answer to Problem 4.1.1P

The equation is $y=\frac{-8x}{3}-8$

Explanation of Solution

Given information: $8x+3y=-24$

Formula Used:Equation of line in terms of slope and intercept,

  $y=mx+c$

Calculation:

Shifting left-hand side variables to right-hand side,

  $3y=-8x-24$

Cross-multiplying both sides,

  $y=\frac{-8x-24}{3}$

On solving,

  $y=\frac{-8x}{3}-8$

Conclusion:The equation is $y=\frac{-8x}{3}-8$

c.

To determine

To graph the equations and tell the common point

Explanation of Solution

Given information: $y=\frac{-8x}{3}-8$

And $y=\frac{4}{5}x-8$

Graph:

The blue line represents $y=\frac{-8x}{3}-8$ and the green line represents $y=\frac{4}{5}x-8$

  

Calculation:

The common point for both the line is (0,-8).

This point on both the graphs shows the initial point of equation, which is, when x is 0.