Question

Using complete sentences, explain how to find the equation of the line, in standard form and slope–intercept form, passing through (3, 6) and (–2, –4). Also compare the benefits of writing an equation in standard form to the benefits of writing an equation in slope–intercept form.

Answer 1

\[ax+by+c=0\]

slope intercept form
\[y=mx+b\]

re-arrange for \(\triangle\) y = m\(\triangle\) x to get point-slope form
\[m=\frac{\triangle y}{\triangle x}=\frac{y_2-y_1}{x_2-x_1}\]

Answer 2

For more about why to use each, this is a pretty decent and brief explanation:
http://answers.yahoo.com/question/index?qid=20060907142906AAsN42o

Answer 3

To get to the slope-intercept form, it is necessary to find the slope of the line, which is given by the formula
\[\frac{y _{2}-y _{1}}{x _{2}-x _{1}}\]
Substituting, we get
\[\frac{-4-6}{-2-3}= \frac{-10}{-5}= 2\]
Your slope m = 2.
The slope intercept form is
y = mx + b, to get this, use the point-slope form to get an equation for the line:
The point slope form, where m is the slope and (a,b) is a point on the line is
y - b = m(x - a)
Choose (-2, -4) for the point, and the slope is 2, the equation of the line in point-slope form is
y + 2 = 2(x + 4)
y = 2x + 8 - 2
y = 2x + 6
And this is the slope intercept form. ( y = 2x + 6 )

The standard form of a linear equation is
Ax + By = C
To get that, one need rearrange the equation so that the terms with x and y are on one side, and the constant, on the other side of the equation.

2x - y = -6
And that's the standard form.

Answer 4

@SourPower
IMPORTANT
I made an ERROR
Please disregard everything after
"Choose (-2, -4) for the point, and the slope is 2, the equation of the line in point-slope form is"
And replace it with this :
y + 4 = 2(x + 2)
y = 2x + 4 - 4
y = 2x
And that's your slope-intercept form (note that your y-intercept is 0, meaning y is 0 when x is 0)

Standard form is
Ax + By = C,
To get to that, it needs to be rearranged:
2x - y = 0
And that's your standard form.