The graph below represents which system of inequalities?
graph of two infinite lines that intersect at a point. One line is solid and goes through the points negative 3, 0, negative 4, negative 1 and is shaded in below the line. The other line is solid, and goes through the points 1, 1, 2, negative 1 and is shaded in below the line.
y ≤ −2x + 3
y ≤ x + 3
y ≥ −2x + 3
y ≥ x + 3
y ≤ −3x + 2
y ≤ −x + 2
y > −2x + 3
y > x + 3
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find "change in y" divided by "change in x"
so it would look like
yes. now simplify
if you write the equation of a line in the form
y = mx + b
m is the slope
in this case
y = 1x + b
y= x+ b
when they say
One line is solid
that means either \( \le \) or \( \ge\)
ok so the answer is D
is shaded in below the line
that means the "y" values are less than or equal to the line
so you should look for
\[ y \le x + b \]
as one of the answers.
cross off any choice that does not have that as an option.
is the B three
y > −2x + 3
y > x + 3
means: 1) the > means the line is dotted.
2) the shaded area is y bigger (i.e. above) the line
so D is wrong two different ways.
ok so its A
we could figure out what b is in
y = x + b
by using one of the points:
replace x with -3 and y with 0
0 = -3 + b
add +3 to both sides
+3 = -3 + 3 + b
so yes , b is 3
Yes. the answer is A
B has the wrong >= sign
and C does not have y <= x + 3
If you wanted, you could find the slope of the second line,
and figure out its equation. But unless there is a typo, it will be
y <= -2x+3
thanks for your help and have a great fourth of july