How many equations have the point (3, 9) located on their graph.

Question

y= x^2

y= 2^x

y= (1/2)x

y= |-3x|

y= -|4x|

y= 2x+ 3

Answer 1

Hi, Yvette.

The graph of an equation is actually the plot of all the solutions of that equation. That means that if you pick a point on the graph of an equation, the coordinates of the point will work in the equation.

This question is looking for the equations that work when x=3 and y=9.

Equation 1:   y = x²         --->          9 = 3²             it works!

Equation 2:   y = 2^x         --->          9 = 2³             no, because 2³ = 8

Equation 3:   y = (1/2)x   --->        9 = 1/2 * 3       no, because 1/2 * 3 = 3/2

Equation 4:   y = |-3x|    --->        9 = |-3 * 3|      it works! |-3 * 3| = |-9|    The absolute value is always the positive value.

You can test the last two equations on your own. The equations that work using (3,9) have that point on their graph.