Chapter 4.2, Problem 42HP

To determine

To find: The equation that does not belong. In other words, which equation is different.

Answer to Problem 42HP

The equation is $y+4=3(x+1)$ .

Explanation of Solution

Given information:

Four equations are given in slope-point form.

Calculation:

Convert each of the four equations in slope-intercept form.

Equation 1 is $y-5=3(x-1)$ So convert it to slope intercept form.

  $\begin{array}{c}y-5=3(x-1)\\ y-5=3x-3\\ y=3x-3+5\\ y=3x+\mathrm{2...}(A)\end{array}$

Equation 2 is $y+1=3(x+1)$ So convert it to slope intercept form.

  $\begin{array}{l}y+1=3(x+1)\\ y+1=3x+3\\ y=3x+3-1\\ y=3x+\mathrm{2...}(B)\end{array}$

  $Equation1is.Soconvertittoslopeinterceptform.$

Equation 3 is $y+4=3(x+1)$ so convert it to slope intercept form.

  $\begin{array}{l}y+4=3(x+1)\\ y+4=3x+3\\ y=3x+3-4\\ y=3x-\mathrm{1...}(C)\end{array}$

Equation 4 is $y-8=3(x-2)$ so convert it to slope intercept form.

  $\begin{array}{l}y-8=3(x-2)\\ y-8=3x-6\\ y=3x-6+8\\ y=3x+\mathrm{2...}(D)\end{array}$

Conclusion:

The result from A, B, C and D, can conclude that Equation 3 i.e. $y+4=3(x+1)$ does not match the rest of the equations.