Chapter ISG, Problem 3.5.3P

To determine

To form an equation for the line.

Answer to Problem 3.5.3P

Equation of planned line is, $y=-11.5x+23$

Equation of actual line is, $y=-8x+23$

Explanation of Solution

Given information:

Graph for P’s actual and planned ride home

For the planned ride (f(x)) line, x- intercept is (2, 0)

y- intercept is (0, 23)

For the actual ride (g(x)) line, x- intercept is (2.8, 0)

y- intercept is (0, 23)

Graph:

Blue line represents f(x) and green line represents g(x)

  

Formula used: Slope is,

  $m=\frac{y2-y1}{x2-x1}$

Equation of line is,

  $y=mx+c$

Calculation:

For planned ride f(x)),

For slope substituting the values in slope formula,

  $m=\frac{23-0}{0-2}$

So,

  $m=-\frac{23}{2}$

On solving,

  $m=-11.5$

For the equation of line, substituting the values,

  $y=-11.5x+23$

For actual ride g(x)),

For slope substituting the values in slope formula,

  $m=\frac{23-0}{0-2.8}$

So,

  $m=-\frac{23}{2.8}$

On solving,

  $m=-8$

For the equation of line, substituting the values,

  $y=-8x+23$