Question

write an equation of the line containing the given point.
(0,8), 7x+4y=9

Answer 1

There are infinite lines that can go through a point. That we can call "line family".
You can take any other point and that point, and create a line that will go through the point you chose and the given point.

Answer 2

ok so how would i find the equstion though

Answer 3

I'll give you one of the many. I'll take "any point", wich means i'll chose the point "G" wich has coordinates (x,y).
So no I have defined a point, I can use both to write a line equation, but let's begin by finding the slope.
\[m=\frac{ y_g-8 }{ x_g-0 }\]
\[m=\frac{ y_g-8 }{ x_g }\]
So, now that we know the slope, we can use the equation that has this form:
\[(y-y_p)=m(x-x_p)\]
yp and xp are the coordinates of any point. but it has to be used by the slope, else this won't work.
I'll chose the point (0,8).
so:
\[(y-8)=m(x-0)\]
x-0 = x , And we have found the slope of the line we are looking for, so let's replace:
\[(y-8)=(\frac{ y_g-8 }{ x_g })(x)\]
So the end result is found by simplifying and putting the equation in a y=mx+b form.
\[y-8=\frac{ (y_g-8)x }{ x_g }\]
So then:
\[y=\frac{ (y_g - 8 )x }{ x_g }+8\]
finally:
\[y=\frac{ (y_g-8)x+8x_g }{ x_g }\]
That must represent the lequation of the line that goes through point (0,8) and any other point. Because Xg ang Yg are any point in the plane.