Question

Help!!

Indicate in standard form the equation of the line passing through the given points.

P(6, 2), Q(8, -4)

Answer 1

remember the genral equation of a line passing through two points
\((x_1,y_1)\;{\rm and}\;(x_2,y_2)\)
is given by\[
\frac{y-y_1}{y_1-y_2}=\frac{x-x_1}{x_1-x_2}
\]

Answer 2

plug in the co-ordinates of the two points in the equation

Answer 3

Standard form requires the form:
Ax+By=C

The first thing we want to do is find the slope of this equation:

Slope is rise/run, or change in y/change in x.
From P to Q, x changes from 6 to 8, a total change of 2.
Likewise, y changes by -6.
Therefore, m=-6/2, or -3 simplified.

The slope m will be the "A" from the formula stated above. The only thing we need to remember is that x is given positive priority. What this means is, you do what you must to make the coefficient for x positive (so A will actually be 3). So far we have:

y=-3x+C

To find C, we have to find the y intercept to turn this two variable equation into a single variable equation. At the y intercept, x=0. We can continue the pattern that the slope gives us to trace our way to that point:

at x=6, y=2 as stated by the points given.
Following this pattern, x=4 must give us y=8 (since for every -2 unit change in x, we have +6 unit change for y).
Eventually we get x=0, y=20, our y intercept.

The y intercept is also the C of our formula, giving us:

y=-3x+20

This, when transformed into standard form, looks like:

-3x-y+20
-3x-y=-20
3x+y=20

This can be checked by plugging in our points, which turn out to work. Hope this helps! If there is any more explanation I can give, just let me know.

Answer 4

Cough