Answer:
y ≤ [tex]\frac{1}{2} x+3[/tex]
Step-by-step explanation:
Since everything below and to the right of the line is shaded, we must have the following:
y ≤
because the symbol ≤ implies that the area below the line is the shaded part
with this, options 3 and 4 are discarded
now, on the right side of the symbol we should have the expression for a line, which as a general form:
[tex]mx+b[/tex]
where m is the slope and b is the y-intercept of the line
so until now the answer should be in the form
y ≤ [tex]mx+b[/tex]
and we calculate the slope m with the two points we are given:
(-4, 1) and (0, 3)
where:
[tex]x_{1}=-4\\y_{1}=1\\x_{2}=0\\y_{2}=3[/tex]
and we plug this values in the slope equation:
[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}} \\\\m=\frac{3-1}{0-(-4)}\\ \\m=\frac{2}{4}\\ \\m=\frac{1}{2}[/tex]
so now we know that our solution must have the form:
y ≤ [tex]\frac{1}{2} x+b[/tex]
and b can be found since we know that the line passes through (0, 3), so when x=0 y=3, this means that the y-intercept b is 3:
y ≤ [tex]\frac{1}{2} x+3[/tex]
which is the second option
