Question

Find an equation for the line with the given properties. Express your answer using either the general form or the slope-intercept form of the equation of a line. slope=-1/2, contain the point (3,-3)

Answer 1

Step 1. We are given the slope of the line. We will call this slope 'm':

$m=-\frac{1}{2}$

We also have the point (3, -3) which we will label as (x1,y1):

$\begin{gathered} x_1=3 \\ y_1=-3 \end{gathered}$

Required: Find the equation for the line.

Step 2. Since we have the slope and a point, we use the point-slope equation:

$y-y_1=m(x_-x_1)$

Substituting the known values:

$y-(-3)=-\frac{1}{2}(x-3)$

We will express our answer in the slope-intercept form:

$y=mx+b$

where m is the slope and b is the y-intercept.

Step 3. To convert our equation into the slope-intercept form, we need to simplify the operations:

$\begin{gathered} y-(-3)=-\frac{1}{2}(x-3) \\ \downarrow \\ y+3=-\frac{1}{2}x+\frac{3}{2} \end{gathered}$

Subtract 3 from both sides:

$\begin{gathered} y=-\frac{1}{2}x+\frac{3}{2}-3 \\ \downarrow \\ \boxed{y=-\frac{1}{2}x-\frac{3}{2}} \end{gathered}$

That is the equation in the slope-intercept form.

Answer:

$\boxed{y=-\frac{1}{2}x-\frac{3}{2}}$