c. 4y -x = 8
each of the equations can be put into slope-intercept form (solved for y) as follows:
a: y = 4x +9
b: y = 4x -8
c: y = (1/4)x +2
d: y = 4x -4
the equations containing the term "4x" all describe parallel lines. the equation containing (1/4)x describes a line that intersects the given line. it is not parallel to the others.
the ray is name from the point to the arrow
in order for three line segments to form a triangle with non-zero area, they must satisfy the "triangle inequality." there are several ways to express this, but perhaps the simplest is
a + b > c
where a, b, and c are the lengths of sides in order from shortest to longest.
here, that means the requirement for a triangle is
4 + 4 > 7 . . true, so a triangle can be formed
the triangle inequality is satisfied by these segment lengths.
f(x) -4 shifts it down 4 units from f(x)
when we add or subtract from f(x) this causes a shift in the vertical direction.
when we add it shifts it up.
when we subtract is shifts it down
f(x) -4 shifts it down 4 units