Chapter SH, Problem 4.2EP

To determine

To write in slope intercept form for the line that passes through the point $(9,6)$ and has the slope $\frac{1}{3}$ .

Answer to Problem 4.2EP

The slope intercept form is $y=\frac{1}{3}x+3$

Explanation of Solution

Given information:

The line that passes through the point $(9,6)$

And has the slope $\frac{1}{3}$ .

Calculation:

Slope intercept form: The graph of the equation $y=mx+b$ (where m and b are real numbers) is a line with slope, m, and y-intercept, b.This form of the equation of a line is called the slope-intercept form.

Formation of point $(9,6)$ and slope, $\frac{1}{3}$ into slope intercept form

  $x_1=9$

  $y_1=6$

  $m=\frac{1}{3}$

Slope intercept form when point and slope is given is

  $y-y_1=m(x-x_1)$

Substituting value of x, y, and m in the slope intercept form

  $y-6=\frac{1}{3}(x-9)$

So,

  $y=\frac{1}{3}x-3+6$

On solving,

  $y=\frac{1}{3}x+3$

Hence, the slope intercept form is $y=\frac{1}{3}x+3$