We have a line that passes through point (0,3) and (-4,0).
Slope-intercept form:
We can calculate the slope of the line as:
[tex]m=\frac{\Delta y}{\Delta x}=\frac{y_2-y_1}{x_2-x_1}=\frac{0-3}{-4-0}=\frac{-3}{-4}=\frac{3}{4}[/tex]The y-intercept can now be calculated using the slope and one of the points:
[tex]\begin{gathered} y=mx+b \\ 3=\frac{3}{4}\cdot0+b=0+b=b \\ b=3 \end{gathered}[/tex]Then, we can express the equation as:
[tex]y=\frac{3}{4}x+3[/tex]Direct variation:
We can not express as a direct variation line as the line do not go through the origin.
Point-slope form:
This form is:
[tex]y-y_1=m(x-x_1)[/tex]We have to know the slope and one point in order to be able to write it.
The slope is 3/4 and one of the points is (0,3). We can write it as:
[tex]y-3=\frac{3}{4}(x-0)[/tex]Two intercept form:
This form is:
[tex]ax+by=c[/tex]We can write this for our case as:
When x=0, y=c/b=3, and when y=0, x=c/a=-4.
We can write that c=1, and then b=1/3 and a=-1/4.
Then, our equation becomes:
[tex]\frac{-1}{4}x+\frac{1}{3}y=1[/tex]If we multiply both sides by 12 (the common factor of 3 and 4), we would get:
[tex]-3x+4y=12[/tex]that is equivalent to the previous equation.