Answer:
OPTION A.
OPTION D.
OPTION E.
Step-by-step explanation:
The equation of the line in Slope-Intercept form is:
[tex]y=mx+b[/tex]
Where "m" is the slope and "b" is the y-intercept.
The Standard form of the equation of the line is:
[tex]Ax + By = C[/tex]
Where "A" is a positive integer, and "B" and "C" are integers.
Choose two points from the table and find the slope with this formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex].
Points:
[tex](1,27)\\\\(4,24)[/tex]
So we get that the slope is:
[tex]m=\frac{24-27}{4-1}=-1[/tex]
Let's substitute the slope and the coordinates of the point (1,27) into [tex]y=mx+b[/tex] and then solve for "b":
[tex]27=(-1)(1)+b\\\\27+1=b\\\\b=28[/tex]
Then, we get that the equation of the line in Slope-Intercept form is:
[tex]y=-x+28[/tex] or [tex]28-x=y[/tex]
In order to write it in Standard form, we can add "x" to both sides of the equation:
[tex]y+x=-x+28+x\\\\x+y=28[/tex]
We can solve for "x" by subtracting "y" from both sides of the equation:
[tex]x+y-y=28-y\\x=28-y\\\\28-y=x[/tex]
