Chapter 4, Problem 4CT

To determine

Write an equation of the line in slope-intercept form.

Answer to Problem 4CT

The equation of the line is $y=-3x+6$ .

Explanation of Solution

Given information:

Line is passes through (0,6) and (3,-3).

Calculation:

Formula :

In general slope intercept equation of a line is,

  $y=mx+b$ ….1

where $m$ is the slope of the line and $b$ is the y-intercept.

Finding $m$:

The slope of the line or a linear function is the ration of the change of $y$ over the change in $x$ between any two points on the line .To find the slope between the points (0,6) and (3,-3)

  $\begin{array}{c}\text{slope=change}\text{in}y/\text{change}\text{in}x.\\ m=(y_{2-}{y}_1)/(x_2-x_1).\\ m=-3-6/(3-0).\\ m=-9/3\\ m=-3.\end{array}$

Substituting $m=-3$ in equation (1),

  $y=-3x+b.$ ................(2)

Finding $b$:

Since given point is (0,6) so substituting 0 for $x$ and 6 for $y$ in equation (2).

  $\begin{array}{l}6=-3\times 0+b\\ b=6.\end{array}$

Substituting the $b=6$ in equation (2),

  $y=-3x+6$ so,

The equation of the line passes through (0,6) and (3,-3) is $y=-3x+6$ .