Answer:
D
Step-by-step explanation:
from the picture, we know that the slope is negative to begin, since the line is going on a downward direction from left to right. this eliminated A and C instantly.
Now we also can see the graph crossed at 3 for the y intercept, which is another reason to eliminate A and C.
we must then find the show of the line.
let us use to point (0,3) since this is the y intercept and (6,0) since this is the x intercept. to find the slope, m, at must use the equation
[tex]m = \frac{y2 - y1}{x2 - x1} [/tex]
so, let's label (0,3) as point 1 and (6,0) as point two. then,
x1 = 0
y1= 3
and
x2= 6
y2=0
Now we just plug in and simplify.
[tex] m = \frac{0 - 3}{6 - 0} = \frac{ - 3}{6} = - \frac{1}{2} [/tex]
we now have our slope and y intercept, so we can plug them into our equation
[tex]y = mx + b[/tex]
where m is the slope and b is the y intercept.
our equation is thus
[tex]y = - \frac{1}{2} x + 3[/tex]
so, the answer is D
