Chapter 4.1, Problem 66HP

To determine

To Explain:

How you would use a given y-intercept and the slope to predict a y-value for a given x-value without graphing.

Answer to Problem 66HP

If the slope is m and the y-intercept is b, substitute the given x-values for x in

  $y=mx+b$ and then simplify.

Explanation of Solution

Formula Used:

Equation of slope-intercept form of a line is given by:

  $y=mx+b\mathrm{............................}(1)$

Where

  $\begin{array}{l}b=y-\mathrm{int}ercept\\ m=\frac{rise}{run}=rate\_of\_change=slope=\frac{y_2-y_1}{x_2-x_1}\mathrm{................}[if(x_1,y_1)\&(x_2,y_2)lie\_on\_line]\end{array}$

Calculation:

If

  $\begin{array}{l}m=slope\\ b=y-\mathrm{int}ercept\\ \end{array}$

Then the slope-intercept form is given by :

  $y=mx+b$

For a given value of x , we can substitute that value in the above equation and simplify it for y .

For example,

  $\begin{array}{l}If\\ m=4\\ b=12\\ x=3\end{array}$

Then the slope-intercept form is :

  $\begin{array}{l}y=4x+12\\ \Rightarrow y=4(3)+\mathrm{12..............}[x=3]\\ \Rightarrow y=12+\mathrm{12.................}[simplify]\\ \Rightarrow y=24\end{array}$