We are told the y-intercept is 1 because the graph goes through (0,1). Now we need to find the slope of the line. Let (3,0) be (x₁,y₁) and (0,1) be (x₂,y₂)
m = y₂ - y₁ / x₂ - x₁
m = 1 - 0 / 0 -3
m = 1 / -3
[tex]m = -\frac{1}{3}[/tex]
Now we have the line's slope and intercept and we put them together in slope intercept form
[tex]y = -\frac{1}{3}x + 1[/tex]
The last think to do is find where it's true. The line is solid so we either ≤ or ≥.(0,0) is shared so (0,0) is a true point.
y = -1/3x +1
0 ? -1/3(0) + 1
0 ? 0 + 1
0 ? 1
≤ makes the inequality true.
Therefore the line given is [tex]y \leq -\frac{1}{3}x +1[/tex]
