The table below represents a function.

what could be the equation of the function?

Choice C.  y = -1.5x

Explanation:

Pick any two rows from the table to form the (x,y) points. I'll pick the first two rows.

Use the slope formula to find the slope of the line through (-6,9) and (-4,6)

m = (y2-y1)/(x2-x1)

m = (6-9)/(-4-(-6))

m = (6-9)/(-4+6)

m = -3/2

m = -1.5

Of the four answer choices, only choice C has a slope of -1.5 so that must be the final answer. Note how the y intercept is b = 0 due to the point (0,0).

So y = -1.5x can be written as y = -1.5x+0; however, it's easier to go with the first option.

As a check, let's try something like x = 2

y = -1.5x

y = -1.5*2

y = -3

This verifies the second to last row of values. I'll let you check the other rows.

Answer: question no. 1 -a. yes, the sides are in the ratio 2 : 5.question no. 2 -b. 59°question no. 3 -c. angles x and y are remote interior angles.question no. 4 -d. 90°, 45° and 45°question no. 5 -b. mn and qrstep-by-step explanation: question no. 1 -rs : xu = 3 : 7.5 = 2 : 5rt : x? = 6.4 : 16 = 2 : 5st : u? = 6 : 15 = 2 : 5as the ratios of all sides are equivalent, the triangles must be congruent and the sides must be proportional.therefore, the answer is: a. yes, the sides are in the ratio 2 : 5.question no. 2 -in the second diagram, angle b is the only letter not shown. therefore, the number must be equivalent to angle b.if we substitute the value of angle b as being 22° in the first diagram, we can now use the angle sum of a triangle to obtain the value of angle a.angle sum of a triangle = 180°therefore: let angle a = aa + 99 + 22 = 180a = 180 - 99 - 22a = 59°therefore, the answer is: b. 59°question no. 3 -angles x and y don't share the vertex of the triangle with the exterior angle w. remote interior angles don't share a vertex of a triangle with an exterior angle. this means that angles x and y are remote interior angles.therefore, the answer is: c. angles x and y are remote interior angles.question no. 4 -the sum of all interior angles of a triangle must be equivalent to 180°.90°, 45° and 45° are the only set of angle measures that are equivalent to 180°.therefore, the answer is: d. 90°, 45° and 45°question no. 5 -the only pair of sides stated in the options which are corresponding are mn and qr.therefore, the answer is: b. mn and qr.