the slope intercept form of a linear equation is y = mx + b.
m is the slope.
b is the y-intercept.
the y-intercept is the value of y when the value of x is 0.
that's the point where the graph crosses the y-axis.
the standard form of a linear equation is ax + by = c
a is the coefficient of the x term.
b is the coefficient of the y term.
c is the constant term.
first we'll work with the slope intercept form of the equation.
then we'll convert that form to the standard form.
the slope intercept form of the equation is y = mx + b.
m is the slope and b is the y-intercept.
we'll have 2 equations.
one of them crosses the y-axis at y = 3.
the other crosses the y-axis at y = -4.
your two equation will be:
y = mx + 3
y = mx - 4
we replaced b with the y-intercepts that we saw on the graph.
now we look at the slope.
the line that crosses the y-axis at 3 is sloping downward from left to right.
this tells us the slope will be negative.
it starts at the point (0,3) which is the y-intercept.
we look for the next intersection that is an integer.
there are 3 that we can see.
they are at (1,2), (2,1), and (3,0).
i chose the point (3,0) to calculate the slope.
the two points i chose are (0,3) and (3,0).
let (x1,y1) = (0,3)
let (x2,y2) = (3,0)
slope = (y2-y1)/(x2-x1) = (0-3)/(3-0) = -3/3 = -1.
replace m with -1 in the equation that has 3 as the y-intercept and you get y = -x + 3.
a similar analysis in the line that intersects the y-axis at -4 uses the points (0,-4) and (3,-1) going from left to right.
let (x1,y1) = (0,-4)
let (x2,y2) = (3,-1)
slope = (y2-y1)/(x2-x1) = (-4-(-1))/(3-0) = (-4+1)/3 = 3/3 = 1.
replace m with 1 in the equation of the line with the y-intercept of -4 to get y = x - 4.
your equations are y = -x + 3 and y = x - 4.
the graph has a shaded region and the lines are dashed.
this indicates an inequality of > or <, but not >= or <=.
if it was >= or <=, the lines would be solid.
since they are dashed, the inequality is < or >.
the shaded region is under the line of y = -x + 3, therefore the equation is y < -x + 3.
the shaded region is above the line y = x - 4, therefore the equation is y > x - 4.
to convert these equations to standard form, do the following:
start with y < -x + 3
add x to both sides of the equation to get x + y < 3.
start with y > x - 4
subtract x from both sides of the equation to get -x + y > -4
your equations are x + y < 3 and -x + y > -4.
that would be selection D.